Available Microtutorial Videos
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TITLE | MATHEMATICAL TOPIC(S) | RELATED SUBJECT AREA(S) | SOURCE |
---|---|---|---|
MRI Depreciation |
Linear Functions; Linear Depreciation; Business Applications |
Social Sciences |
Problem 90, page 33 found in R. Larson. Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Soda Manufacturer |
Linear Functions; Linear Cost Function; Fixed Cost; Marginal Cost; Business Applications |
Social Sciences |
Problem 82, page 99 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Housing Development Revenue |
Quadratic Function Models; Demand Function; Revenue Function; Business Applications |
Social Sciences |
Problem 33, page 143 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Manufacturing Profit |
Piecewise-Defined Functions; Demand, Revenue, Cost, and Profit Functions; Business Applications |
Social Sciences |
Problem 76, page 47 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Gene Regulation |
Squeeze Theorem; Sandwich Theorem; Limits |
Biological; Mathematical |
Problem 32, page 136 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Oscillating Population |
Squeeze Theorem; Sandwich Theorem; Limits; Limit at Infinity |
Mathematical |
Problem 12, page 130 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd Edition, Prentice Hall, Pearson, 2011.” |
Continuity of a Piecewise-Defined Function |
Continuity and One-Sided Limits; Left Continuous; Right Continuous; Piecewise-Defined Functions |
Mathematical |
Problem 49, page 83 found in “J. Rogawski and C. Adams. Calculus, 3rd edition, W. H. Freeman and Company, New York, 2015.” |
Movie Advertising |
Continuity and One-Sided Limits; Piecewise-Defined Functions; Business Applications |
Social Sciences |
Problem 91, page 237 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Gravitational Force |
Continuity and One-Sided Limits; Limits; Piecewise-Defined Functions |
Physical; Mathematical |
Problem 36, page 148 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Sciences, Cengage Learning, 2015.” |
Fungal Growth |
Continuity and One-Sided Limits; Limits; Graph of Piecewise-Defined Functions |
Biological; Mathematical |
Problem 50, page 120 found in C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018. |
Salt Concentration |
Limits at Infinity; Mixture Problem |
Physical |
Exercise 34, page 110 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Falling Raindrop |
Limits at Infinity; Terminal Velocity |
Physical |
Exercise 37, page 111 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Predator-Prey Model |
Limits at Infinity; Horizontal Asymptote |
Biological |
Adapted from Problem 15, page 130 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Prentice Hall, 2011.” |
Population Size |
Limits at Infinity; |
Biological; Mathematical |
Problem 11, page 130 found in C. Neuhauser, Calculus for Biology and Medicine, Third edition, Pearson 2011. |
Reaction Rates of Enzymes and Substrates |
Limits at Infinity; Evaluating Limits |
Physical |
Problem 33, page 99 found in “J. Rogawski, C. Adams. Calculus Early Transcendentals, 3rd edition, Macmillin, 2015.” |
Crude Oil Prices | Average Rate of Change; Business Applications | Social Sciences |
Problem 43, page 252 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Metabolizing Acetaminophen | Average and Instantaneous Rates of Change; Difference Quotient; Definition of the Derivative | Biological |
Problem 1.2.5, page 25 found in “G. Ledder. Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems, 1st edition, Springer, New York, 2013.” |
Drop The Tool |
Limits; Position & Velocity Functions; Instantaneous Velocity |
Physical |
Problems 103 and 104, page 69 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Logistic Growth | Rate of Change; Carrying Capacity; Population Growth & Equilibrium | Biological | Neuhauser, Calculus for Biology and Medicine, 3rd edition, Pearson Education, 2011 Problem 49, page 145 |
Biotic Diversity | Application of Derivatives; Rates of Change; Ecosystem Equilibrium | Biological |
Problem 50, page 145 found in Claudia Neuhauser. Calculus for Biology and Medicine, Third Edition, Pearson, 2011. |
Highway Design | Derivative as Slope of a Tangent Line; Quadratic Function | Physical |
Exercise 64, page 171 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Lizard Energy Expenditure | Applications of Derivatives; Differentiation Rules | Biological; Physical |
Problem 47, page 595 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, 2015 Cengage Learning.” |
Body Surface Area | Rates of Change; Interpretation of the Derivative | Biological |
Problem 35, page 149 found in “J. Rogawski, C. Adams. Calculus Early Transcendentals, 3rd edition, Macmillin, 2015.” |
T-Shirts for Sale | Rates of Change; Derivative; Revenue Function; Business Applications | Social Sciences |
Problem 81, page 340 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Water Snakes | Derivatives as Rates of Change; Interpreting Derivative | Biological |
Problem 49, page 183 found in R.N. Greenwell, N.P. Ritchey, M.L. Lial, Calculus for the Life Sciences, Pearson, 2nd edition. |
Dead Sea | Derivative and Instantaneous Rate of Change; | Physical |
Problem 72, page 213 found in “R.N. Greenwell, N.P. Ritchey, M.L. Lial, Calculus for the Life Sciences, 2nd edition, Pearson, 2015”. |
Marginal Profit | Derivative and Marginal Profit; Demand, Revenue, Cost, and Profit Functions; Business Applications | Social Sciences |
Problem 40ac, page 116 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Median Home Prices | Average Vs Instantaneous Rate of Change; Derivatives; Business Applications | Social Sciences |
Problem 88, page 274 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Plaque in Arteries | Derivative and Instantaneous Rate of Change; | Biological |
Problem 33, page 230 found in "S. Schreiber, K. Smith, and W. Getz. Calculus for the Life Sciences, 1st Edition, John Wiley & sons, 2014." |
Biomass | Product Rule; Derivative as Rate of Change; Fish Population | Biological |
Problem 56, page 202 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Inventory Replenishment | Quotient Rule; Derivatives; Rate of Change; Cost Function; Marginal Cost; Business Applications | Social Sciences |
Problem 71, page 126 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Tip Speed Ratio | Quotient Rule; Derivatives; Rate of Change | Physical |
Page 141 Problem 52 in “J. Rogawski and C. Adams. Calculus, 3rd edition, W. H. Freeman and Company, New York, 2015.” |
Insecticide Resistance | Quotient Rule; Derivatives; Rate of Change | Biological |
Problem 54, page 201 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Gas Consumption | Product and Quotient Rules; Derivatives; Rate of Change | Physical |
Problem 59, page 141 found in “D. Hughes-Hallett; A. Gleason; W. McCallum. Calculus, Single & Multivariable, 6th Edition, Wiley & Sons, Inc.” |
Body Mass Index | Quotient Rule; Chain Rule; Derivative as Rate of Change | Biological |
Problem 67 and 68 pg 223, Calculus and its Applications by Goldstein, Lay, Asmar, Schneider. Ed 13 Pearson. |
Nursing School Woes | Differentiation; Proportionality; Derivative as Rate of Change | Biological |
Neuhauser, Calculus for Biology and Medicine, 3rd edition, Pearson Education, 2011 Problem 72, page 173 |
Sinus Pressure | Chain Rule; Interpretation of the Derivative | Biological | Exercise 56, page 213 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Pollution | Chain Rule; Interpretation of the Derivative | Physical | Greenwell, Ritchey, & Lial, Calculus for the Life Sciences (Second ed.) Problem 56, page 228 |
Wave Motion | Chain Rule; Simple Harmonic Motion | Physical |
Exercise 114, page 139 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Circadian Growth | Derivatives of Trigonometric Functions; Chain Rule; Bound of the Sine Function; Solving Inequalities | Biological; Mathematical |
Problem 74, page 188 found in C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018. |
Big Fish | Limits at Infinity; Exponential Growth; Von Bertalanffy Growth Model | Biological |
Neuhauser, Calculus for Biology and Medicine, 3rd edition, Pearson Education, 2011 Problem 65, page 182 |
It's How Old? | Exponential Growth and Decay; Business Applications | Social Sciences |
Problem 81, page 283 found in “Larson. Calculus: An Applied Approach, 10th edition, Cengage Learning, Boston, 2017.” |
Light Intensity in Water | Exponential Growth and Decay; Differential Equations; Initial Value Problem | Physical |
Modified version of Example 5.5.6, page 256 found in “Calculus For the Life Sciences: A Modeling Approach” by James L. Cornette and Ralph A. Ackerman. Electronic version volume 1. https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=92 |
Radioactive Decay | Exponential Growth and Decay; Derivative of Exponential Function; Half Life; Differential Equations | Physical |
Problem 72, page 183 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Pearson Education, Inc.” |
Genetic Drift | Derivatives of Logarithmic Functions; Chain Rule; Applications of Derivatives; Fruit Flies | Biological |
Problem 30, page 229 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, 2015 Cengage Learning.” |
Travel Time | Position, Velocity, and Acceleration Functions; Applications of Derivatives; Graphical Interpretations of Derivatives | Physical |
Problem 34, page 201 found in C. Neuhauser, Calculus for Biology and Medicine, Third edition, Pearson, 2011. |
Biking Trip | Position, Velocity, and Acceleration; First and Second Derivatives; Graphical Interpretation of the Derivative; Graphs of Trigonometric Functions | Physical; Mathematical |
Problem 33, page 201 found in C. Neuhauser, Calculus for Biology and Medicine, Third edition, Pearson 2011. |
Predation Population | Chain Rule; Implicit Differentiation | Biological |
Problem 56, page 1.6.2 found in “G. Ledder Mathematics for Life Sciences, 1st edition, Springer, New York, 2010.” |
Cobb-Douglas Production Function | Implicit Differentiation; Business Applications | Social Sciences | Problem 47, page 150 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Production Function | Implicit Differentiation; Cobb-Douglas Production Function; Business Applications | Social Sciences | Problem 29, page 448 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Resource Allocation | Implicit Differentiation; Related Rates; Business Applications | Social Sciences | Problem 27, page 448 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Check Out Those Books | Implicit Differentiation | Mathematical; Social Sciences | Problem 48 pg 243, Calculus and its Applications by Goldstein, Lay, Asmar, Schneider. Ed 13 Pearson. |
Energy Consumption | Implicit Differentiation | Biological | Exercise 47, pg. 228 Adler, F. R. (1998). Modeling the dynamics of life: Calculus and probability for life scientists (3rd ed.). Pacific Grove, CA: Brooks/Cole. |
The Blood is A Flowin' | Implicit Differentiation | Biological | Thomas, Calculus, 11th edition, Pearson Education, 2005 Page 220, Problem 25 |
Bacteria Population | Inverse Functions | Biological |
Problem 57, page 67 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, 2015 Cengage Learning.” |
Velocity in a Resisting Medium | L'Hopital's Rule | Physical |
Exercise 93, page 578 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Species Diversity | L'Hopital's Rule; Limits; Continuity | Biological |
Problem 67, page 260 found in "C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018." |
Bus Line Prices | Optimization; Extrema in a Closed Interval; Demand Function and Maximum Revenue; Business Applications | Mathematical; Social Sciences |
Problem 11 pg 186. “Calculus and its Applications”. Goldstein, Lay, Schneider, Asmar. Ed 13 Pearson. |
The Supermarket Struggle | Optimization; Relative Extrema; Business Applications | Social Sciences |
Example 2 pg 173. “Calculus and its Applications”. Goldstein, Lay, Schneider, Asmar. Ed 13 Pearson. |
Farming Strawberries | Optimization; Relative Extrema; Business Applications | Social Sciences |
Problem 37, page 203 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Maximizing Apartment Profits | Optimization; Relative Extrema; Business Applications | Social Sciences |
Problem 20, page 213 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
iPhone Average Cost | Optimization; Minimum cost; Cost Function; Business Applications | Social Sciences |
Problem 13, page 409 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Optimal Speed | Optimization; Minimum cost; Cost Function; Business Applications | Social Sciences |
Adapted from problem 46, page 234 found in “R. Larson, Calculus: An Applied Approach, tenth edition, Cengage Learning, 2017.” |
Used Book Black Market | Optimization; Revenue Function; Maximum Revenue; Business Applications | Social Sciences |
Problem 34, page 411 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Code That Software | Optimization; Relative Extrema; Maximum Revenue; Business Applications | Social Sciences |
Problem 59, page 413 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Tracheal Tube When Coughing |
Absolute Extrema on a Closed Interval |
Biological |
Problem 73 pg 279. “Calculus Early Transendentals”. James Stewart. Ed 6 Brooks/Cole, Cengage Learning. |
National Security | Optimization; Implicit Differentiation | Physical; Mathematical | Thomas, Calculus, 11th edition, Pearson Education, 2005 Problem 138, page 533 |
Max Area | Optimization; First Derivative Test; Extrema | Mathematical | Problem 17, page 245 found in “J. Rogawski and C. Adams. Calculus, 3rd edition, W. H. Freeman and Company, New York, 2015.” |
Nick of Time | Optimization; First Derivative Test; Extrema | Mathematical | Adapted from problem 20, page 245 in Rogawski, Jon and Colin Adams, Calculus: Early Transcendentals; 3rd ed., W. H. Freeman, New York, 2015. |
Pharmacokinetics | L'Hopital's Rule; Limit at Infinity; First Derivative Test; Extrema; Maximum; Minimum | Biological; Mathematical |
Problem 54, page 284 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Epidemic | Application of Extrema; Maxima and Minima; Increasing and Decreasing Functions | Biological | Problem 12, page 222 found in “J. Arya, R. Lardner. Mathematics for the Biological Sciences, Prentice Hall, New Jersey, 1979.” |
Minimizing Energy Expenditure | Optimization; First Derivative Test; Extrema | Biological | Problem 1.5.3, page 47 found in “G. Ledder. Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems, 1st edition, Springer, New York, 2013.” |
Injection Model | Derivatives in Modeling; Critical Points; Extrema | Biological | Problem 60, page 262 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus, 6th edition, John Wiley & Sons, Inc., 2013.” |
The Speeding Ticket | Mean Value Theorem | Mathematical |
Exercise 59, page 177 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Montana Weather | Mean Value Theorem | Mathematical |
Problem 36, page 182 found in “E. Swokowski. Calculus, 5th Edition, Brooks/Cole, Cengage Learning, 1991.” |
Average Velocity | Mean Value Theorem; Velocity; Average Velocity | Mathematical; Physical |
Problem 32, page 322 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Prentice Hall, Pearson, 2011.” |
The Calculus in Music |
Increasing and Decreasing Functions; Rate of Change |
Physical |
Problem 28 pg. 232. “Calculus Early Transcendentals”. James Stewart. Ed 6 Brooks/Cole, Cengage Learning. |
Worm Population Control | Increasing and Decreasing Functions; First Derivative Test | Biological |
Adapted from: Problem 30 page 222 in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Pearson Education, Inc., Boston, MA, 2011.” |
Hamburger Profit | Increasing and Decreasing Functions; First Derivative Test; Maximum Profit; Business Applications | Social Sciences |
Problem 53, page 176 found in R. Larson. Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Fight The Powa | Optimization; First Derivative Test; Extrema | Physical |
Small modification of problem 41, page 264 found in “J. Stewart. Calculus, 6th edition, Thomson Brooks/Cole, 2008.” |
Graph Analysis | Graph of the Derivative; Local Maximum and Minimum; Derivative of Increasing and Decreasing Functions | Mathematical |
Adapted from Exercise 21, page 176 found in “F. Adler. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, 3rd edition, Brooks/Cole, Cengage Learning, 2013.” |
Tracking a Helicopter | Graphical Behavior of Functions; Graph of the Derivative; Position, Velocity and Acceleration Functions | Mathematical; Physical |
Adapted from: Problem 28 page 177 in “J. Adler. Modeling the Dynamics of Life, 3rd edition, Brooks/Cole, Boston, MA, 2013.” |
Spreading the Flu Part 1 | Global Extrema; First Derivative Test; Graph of a Function; Limits at Infinity; L'Hopital's Rule | Biological |
Problem 43, page 402 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus: Single and Multivariable, 6th edition, John Wiley and Sons, Inc., MA, 2013.” |
Monod Growth | Increasing and Decreasing Functions; Limits to Infinity; Horizontal Asymptotes | Biological |
Adapted from Problem 7, page 274 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Prentice Hall, 2011.” |
Nurse Shortage | Relative Extrema; Increasing and Decreasing Functions; First Derivative Test | Social Sciences |
Problem 89, page 262 found in “Tan Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach, 9th edition, Brooks/Cole, CA, 2011.” |
Vascular Branching | Optimization; Critical Points; Extrema; Increasing and Decreasing Functions; Blood Flow; Poiseuille's Law | Biological |
Problem 55, page 247 found in “J. Rogawski, C. Adams. Calculus Early Transcendentals, 3rd edition, Macmillin, 2015.” |
Snell's Law | Optimization; Critical Points; Extrema; First Derivative Test; Velocity of light | Physical |
Problem 54, page 247 found in “J. Rogawski, C. Adams. Calculus Early Transcendentals, 3rd edition, Macmillin, 2015.” |
Dose Response | Point of Inflection; How Derivatives Affect Graphs | Biological |
Exercise 53, page 273 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
US Inflation | Concavity; Rate of Change; Interpretation of a Graph; Business Applications; | Social Sciences |
Problem 65, page 427 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Alligator Teeth | Point of Inflection; Concavity; Derivative of Exponential Function of Exponential Function; Multiple Chain Rule | Biological |
Problem 88, page 297 found in “R.N. Greenwell, N.P. Ritchey, M.L. Lial, Calculus for the Life Sciences, 2nd edition, Pearson, 2015”. |
Drug Surge | Point of Inflection; Exponential Derivatives; | Biological |
Stewart, Calculus, 6th edition, Thomson Brooks/Cole, 2008. Problem 71, page 404 |
Point of Diminishing Return | Point of Inflection; Point of Diminishing Return; Second Derivative; Concavity; Business Application | Social Sciences |
Adapted from problem 89, page 279 found in “S. T. Tan, Applied Calculus for the Managerial, Life, and Social Sciences, eighth edition, Brooks/Cole, Cengage Learning, 2011.” |
Coffee Consumption | Extreme Values; Interpretation of the Second Derivative | Mathematical; Social Sciences |
Problem 30 pg 179. “Calculus and its Applications”. Goldstein, Lay, Schneider, Asmar. Ed 13 Pearson. |
Gompertz? Gompertz Who? | Derivatives and Growth Functions; Derivative of Exponential Functions; Critical Points; Second Derivative; Inflection Points | Biological |
Problem 56, page 223 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus, 6th edition, John Wiley & Sons, Inc., 2013.” |
Per Capita Production | Extrema and the Second Derivative Test; Critical Points; Concavity | Social Sciences |
Problem 16, page 342 found in F. Adler. Modeling the Dynamics of Life, 3rd edition, Brooks/Cole, Cengage Learning, Boston, 2013. |
Allometric Growth | Implicit Differentiation and Concavity; Second Derivative Test; inflection point | Biological |
Problem 43, page 224 found in Nuehauser, C., Calculus for Biology and Medicine, 3rd edition, Pearson, 2013. |
Factoid Machine | Curve Sketching; Critical Points; First Derivative Test; Second Derivative Test; Inflection Points; Concavity | Mathematical |
Problem 29, page 239 found in “F. Adler. Modeling the Dynamics of Life, 3rd edition, Brooks/Cole, Cengage Learning, Boston, 2013.” |
Related Rates on a Cube | Related Rates; Geometrical Interpretation of dV/dx on a Cube | Mathematical | Problem 11, page 180 found in “J. Stewart. Calculus, 6th edition, Thomson Brooks/Cole, 2008.” |
Oil Revenue | Related Rates; Business Applications | Social Sciences | Problem 25, page 447 found in “Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016.” |
Adiabatic Air Expansion | Related Rates; Implicit Differentiation | Physical | Exercise 88, page 214 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Pulling Boats | Related Rates; Implicit Differentiation | Physical | Adapted from a problem in: Stewart, J. (2003). Calculus: Early transcendentals. Belmont, CA: Thomson/Brooks/Cole. |
Fish Growth | Related Rates; Implicit Differentiation; Von Bertalanffy Growth Function | Biological | Exercise 90, page 215 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Unclogging an Artery | Differentials; Relative Change | Biological | Thomas, Calculus, 11th edition, Pearson Education, 2005 Pg 230 Example 8 |
Measuring Disks | Differentials; Continuous Functions; | Mathematical | Problem 30, page 167 found in “F. Adler Modeling the Dynamics of Life: Calculus and Probability for Life Scientists. Third Edition. Brooks/Cole, Cengage Learning. 2013.” Pre-requisite in calculus: |
Springing Survival | Newton's Method | Biological | Exercise 55, page 215 found in “R. Smith, R. Minton. Calculus, Third Edition, McGraw-Hill, 2008.” |
Restate and Integrate | Integrals of Exponential Functions; Initial Value Problem | Mathematical | The Calculus Problem Solver by Dr. H.Weisbecker et al. 1984 Pg 461 #652. |
Medicate Me | Exponential Growth and Decay; Half Life; Initial Value Problem | Biological | Adapted from Example 1, page 197 found in Greenwell, R., & Ritchey, N. (n.d.). Calculus for the life sciences (Second ed.). |
Stone Acceleration | Antiderivatives; Initial Value Problem; Position, Velocity and Acceleration | Physical | Exercise 44, page 311 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Does She Hit the Cow? | Initial-Value Problem; Antiderivative; Indefinite Integral; Position, Velocity and Acceleration | Physical | Problem 53, page 357 found in "S. Schreiber, K. Smith, and W. Getz. Calculus for the Life Sciences, 1st Edition, John Wiley & sons, 2014." |
Population Dynamics | Initial-Value Problem; Antiderivative; Indefinite Integral; Fundamental Theorem of Calculus | Physical | Problem 10, page 275 found in C. Neuhauser, Calculus for Biology and Medicine, Third edition, Pearson 2011. |
Uploads to YouTube | Initial-Value Problem; Antiderivative; Indefinite Integral; Business Applications | Social Sciences | Problem 52, page 483 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
DirecTV Revenue | Initial-Value Problem; Antiderivative; Indefinite Integral; Business Applications | Social Sciences | Problem 56, page 337 found in “R. Larson. Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017.” |
Length of a Fish | Average Value of a Function and Initial-Value Problem; Antiderivative; Indefinite Integral; Fundamental Theorem of Calculus | Biological | Problem 18, page 400 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, 2015 Cengage Learning.” |
Paying Down a Mortgage | Definite Integral; Business Applications | Social Sciences | Problem 40 pg 337, Calculus and its Applications by Goldstein, Lay, Asmar, Schneider. Ed 13 Pearson. |
iPhone Profit | Definite Integral; Business Applications | Social Sciences | Problem 59, page 525 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Polluted Lake | Definite Integral | Physical | Problem 63, page 408 found in “R.N. Greenwell, N.P. Ritchey, M.L. Lial, Calculus for the Life Sciences, 2nd edition, Pearson, 2015”. |
Stream of Trout | Definite Integral; Integral of an Absolute Value Function | Biological |
Exercise 9, page 418 found in “F. Adler. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, 3rd edition, Brooks/Cole, Cengage Learning, 2013.” |
Total Distance Traveled | Definite Integral; Integral of an Absolute Value Function | Physical | Problem 46 pg 360, Calculus and its Applications by Goldstein, Lay, Asmar, Schneider. Ed 13 Pearson. |
Pool Pump | Definite Integral; Work Done by a Variable Force | Physical | Problem 20, page 373 found in “J. Stewart. Calculus, 6th edition, Thomson Brooks/Cole,2008.” |
Beehavior | Riemann Sum | Mathematical | Adapted from exercise 33, page 387, found in “F. Adler. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, 3rd edition, Brooks/Cole, Cengage Learning, 2013.” |
Cardiac Output Formula | Riemann Sum; Deriving an Integral Formula | Biological; Mathematical | Adapted from page 403 in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Plant Density | Application of Definite Integrals; Riemann Sum; Population Density; Integrating over an Annulus | Biological; Mathematical | Problem 1.7.7, page 66 found in “G. Ledder. Mathematics for the Life Sciences, 1st edition, Springer, New York, 2010.” |
Integrate These Cookies | Definite Integral; Average Value Theorem | Physical; Mathematical | R. Larson, R. Hostetler, B. Edwards, Calculus: with analytic geometry, 6th edition, Houghton Mifflin Company, 1998 Problem 61, page 284 |
Rainfall | Mean Value Theorem; Average Value Theorem; Definite Integral | Physical; Mathematical | Problem 21, page 350, found in "C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018." |
Average Balance | Average Value of a Function; Definite Integral; Piecewise-Defined Function; Business Application | Social Sciences | Problem 44, page 566 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Animal Survival | Definite Integral; Survival Rate; Population Growth | Biological | Problem 1, page 404 found in “J. Stewart, T. Day, Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015." |
How to Manage Equipment Effectively | Fundamental Theorem of Calculus; Depreciation and Business Applications | Mathematical; Social Sciences | Stewart Calculus, 6th edition, Thomson Brooks/Cole, 2008. Problem 67, page 323 |
Particle Motion | Fundamental Theorem of Calculus; Definite Integral; Bounds; Position; Velocity; Acceleration | Physical; Mathematical |
Problem 23, page 179 found in “D. Hughes-Hallett; A. Gleason; W. McCallum, Calculus, Single & Multivariable, 6th edition, Wiley & Sons, Inc.” |
Sludge in a Lake | Integrating Rates of Change; Definite Integral; Units | Physical |
Problem 19, page 295 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus, 6th edition, John Wiley & Sons, Inc., 2013.” |
Population Growth | Integration by Substitution; Exponential Antiderivatives | Biological |
Greenwell, Ritchey, & Lial, Calculus for the Life Sciences (Second ed.) Problem 62, page 384 |
Valuing Lottery Winnings | Future Value; Annuity; Definite Integral; Integration by Substitution; Integral of Exponential Functions; Business Applications | Social Sciences |
Problem 74, page 385 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Saving for College | Future Value; Annuity; Continuous Income Stream; Definite Integral; Integral of Exponential Functions; Business Applications | Social Sciences |
Problem 48, page 578 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |
Stock Exchange | Integration by Substitution; Average Value | Mathematical; Social Sciences |
Greenwell, Ritchey, & Lial, Calculus for the Life Sciences (Second ed.) Problem 45, page 452 |
Oil Leak | Fundamental Theorem of Calculus; Integration by Substitution | Physical |
Problem 64, page 408 found in Greenwell, R., & Ritchey, N. (n.d.). Calculus for the life Sciences (Second ed.) |
Crime Scene | Exponential Growth and Decay; Newton's Law of Cooling; Initial Value Problem (17 minutes) |
Biological; Physical | Adapted from Exponential Growth and Decay. (n.d.). Retrieved January 12, 2016, from http://www.chaoticgolf.com/ |
Revenue for Calculators | Integration by Parts; Business Applications | Mathematical; Social Sciences |
Greenwell, Ritchey, & Lial, Calculus for the Life Sciences (Second ed.) Problem 56, page 445 |
City Size | Integration by Parts | Social Sciences |
Robert Willett, UC Riverside. |
Rumen Micorbial Ecosystem | Integration by Parts | Biological |
Exercise 34, page 367 found in “J. Stewart and T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, 2015.” |
Lightbulb Energy | Trigonometric Integral; Definite Integral; Energy; Power; Voltage; Resistance | Physical |
Problem 76, page 386 found in “J. Rogawski, C. Adams. Calculus: Early Transcendentals, 3rd Edition, W. H. Freeman and Company, Macmillan, 2015.” |
Electric Field from a Charged Wire | Integration by Trigonometric Substitution | Physical |
Adapted from Problem 55, page 392 found in “J. Rogawski, C. Adams. Calculus Early Transcendentals, 3rd edition, Macmillin, 2015.” |
Curbing the Mosquito Population | Integration by Partial Fraction Decomposition | Biological |
Adapted from: Problem 24, page 371 found in “J. Stewart, T. Day. Biocalculus: Calculus for the Life Sciences, Cengage Learning, Boston, 2015.” |
Chemical Reactions | Integration by Partial Fraction Decomposition | Physical |
Adapted from exercise 50, page 580 found in “Thomas’ Calculus, 11th edition, Pearson Addison Wesley, 2004.” |
Rumor in School | Integration by Partial Fraction Decomposition; Definite Integral | Mathematical; Social Sciences |
Problem 78, page 386 found in “D. Hughes-Hallett; A. Gleason; W. McCallum. Calculus, Single & Multivariable, 6th Edition, Wiley & Sons, Inc.” |
Telephone Line | Derivative of Hyperbolic Functions | Physical |
Problem 51, page 260 found in “J. Stewart. Calculus: Early Transcendentals, 6th Edition, Thomson Learning Inc, 2008.” |
Hanging a Cable | Integral of Hyperbolic Functions; Arc Length of a Catenary | Physical |
Adapted from Problem 64, page 323 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Prentice Hall, 2011.” |
Into Orbit |
Improper Integral; Work |
Physical |
Problems 85, page 589 found in “R. Larson and B. Edwards. Calculus, 9th edition, Brooks/Cole, Cengage Learning, 2010.” |
Spreading the Flu Part 2 |
Improper Integral; Integration by parts |
Biological |
Problem 43, page 402 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus: Single and Multivariable, 6th edition, John Wiley and Sons, Inc., MA, 2013.” |
Drug Reaction |
Improper Integral; Integration by parts |
Biological |
Problem 44, page 457 found in R.N. Greenwell, N.P. Ritchey, M.L. Lial, Calculus for the Life Sciences, Pearson, 2nd edition. |
Capacity of a Capacitor |
Improper Integral; |
Physical |
Adapted from problem 83, page 423 in Rogawski, Jon and Colin Adams, Calculus: Early Transcendentals; 3rd ed., W. H. Freeman, New York, 2015. |
Planck's Radiation Law |
Improper Integrals and the Comparison Test; Limits; Convergence; Divergence |
Physical; Mathematical |
Adapted from: Problem 30, page 407 found in “Hughes-Hallett, Gleason, McCallum, et al. Calculus, 6th edition, John Wiley & Sons, Inc., 2013.” |
Cellular Response |
Improper Integrals and the Comparison Test; Convergence; Divergence |
Biological; Mathematical |
Problem 47, page 398 found in "C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018." |
Consumer and Producer Surpluses | Area Between Two Curves; Applications of Definite Integrals; Business Applications | Social Sciences |
Problem 57, page 359 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Savings |
Area Between Curves; Marginal Costs and Savings |
Mathematical; Social Sciences |
Problem 37, page 418 found in Greenwell, R., & Ritchey, N. (n.d.). Calculus for the Life Sciences (Second ed.). |
Y Area Between Curves | Area Between Curves; Integral of x = f(y) | Mathematical | Thomas, Calculus, 11th edition, Pearson Education, 2005 Page 416, Problem 35 |
Area of a Circular Sector | Area Under a Curve; Integration by Trigonometric Substitution | Mathematical | Problem 35 page 509 in “J. Stewart. Single Variable Calculus, 6th edition, Thompson Brooks/Cole, Belmont, CA, 2008.” |
Solar Eclipse | Area between curves; Area of a Lune | Physical; Mathematical | Problem 41, page 509 found in “J. Stewart. Single Variable Calculus, 6th edition, Thompson Brooks/Cole, Belmont, 2008.” |
Lake Mead | Volume by Cross Section; Volume by Slicing; Definite Integral | Physical; Mathematical | Problem 36, page 421 found in “D. Hughes-Hallett; A. Gleason; W. McCallum. Calculus, Single & Multivariable, 6th edition, Wiley & Sons, Inc., 2013” |
A Baseball in the Punchbowl | Volume by Cross-Sectional Area | Physical | Problem 68, page 364 found in “J. Stewart. Calculus, 6th edition, Brooks/Cole, Belmont, CA, 2008.” |
Bowl of Water | Volumes of Revolution; Disc Method; Fundamental Theorem of Calculus; Chain Rule | Physical | Problem 59, page 430 found in “D. Hughes-Hallett; A. Gleason; W. McCallum. Calculus, Single & Multivariable, 6th Edition, Wiley & Sons, Inc.” |
Toast of the Town | Volumes of Revolution; Washer Method | Physical; Mathematical | John Simanyi, UC Riverside. |
Draining a Radio Telescope | Volume by Shell Method; Cylinders of Revolution | Physical | John Simanyi, U C Riverside. |
Napkin Rings | Volume by Cylindrical Shells | Physical | Problem 46, page 437 found in “J. Stewart. Calculus: Early Transcendentals, 6th Edition, Thomson Learning Inc, 2008.” |
Area of a Satellite Dish | Surface Area of a Solid of Revolution | Mathematical; Physical | Problem 28 page 574 in “J. Stewart. Single Variable Calculus, 6th edition, Thompson Brooks/Cole, Belmont, CA, 2008.” |
World's Largest Doughnut | Surface Area of a Torus; Integration by Trigonometric Substitution | Mathematical; Physical | Robert Willett, UC Riverside. |
Determining Length of Fish | Separable Differential Equation; Von Bertalanffy Equation; Asymptotic Length; Limit at Infinity | Biological | Problem 23, page 404 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Pearson Education, Inc.” |
Fish Population | Separable Differential Equation; Equilibrium; Stability; Logistic Growth; Fish Population | Biological | Problem 9, page 418 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Pearson Education, Inc.” |
Insulin Pump | Separable Differential Equation; Integration by Substitution; Initial Condition; Limit at Infinity | Biological | Problem 26, page 439 found in C. Neuhauser and M. Roper. Calculus for Biology and Medicine, 4th Edition, Prentice Hall, Pearson, 2018. |
Allee Effect | Equilibrium and Stability; Eigenvalue Method; Graphical Method; Differential Equations | Biological | Problem 24, page 420 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Prentice Hall, Pearson, 2011.” |
Single Compartment Model | Single Compartment Model; Separable Differential Equations; Equilibrium; Stability; Change in Concentration | Physical | Problem 13, page 419 found in “C. Neuhauser. Calculus for Biology and Medicine, 3rd edition, Pearson Education, Inc.” |
Marginal Utility | Partial Derivatives; Marginal Utility; Business Application | Social Sciences | Problem 73, page 454 found in R. Larson, Calculus: An Applied Approach, 10th edition, Cengage Learning, 2017. |
Fences | Lagrange Multiplier; Partial Derivatives; Business Application | Social Sciences | Problem 21, page 653 found in Waner and Costenoble. Applied Calculus, 7th Edition, Cengage Learning, Boston, 2016. |