# Fall 2021: MAT A29 Calculus I for the Life Sciences

From the Course Calendar: A course in differential calculus for the life sciences. Algebraic and transcendental functions; semi-log and log-log plots; limits of sequences and functions, continuity; extreme value and intermediate value theorems; approximation of discontinuous functions by continuous ones; derivatives; differentials; approximation and local linearity; applications of derivatives; antiderivatives and indefinite integrals.

## Resources

- Differential Calculus for the Life Sciences by Dr. Leah Keshet of UBC.
- OpenStax Calculus 1
- 3Blue1Brown: The Essence of Calculus

## Grading Scheme

Task | Weight |
---|---|

Exam | 40 % |

Term Test | 3x15 % |

Assignments | 5x3 % |

### Exam

### Term Tests

### Assignments

## Learning Objectives

(There are three learning objectives per high-level section of the course.)

- Use graphs to investigate quantitative relationships.
- Evaluate limits numerically, visually, and algebraically.
- Apply the rules of differentiation to algebraic and transcendental functions.

## Schedule of Tasks

Week | Task | Notes |
---|---|---|

1 | ||

2 | A1 | |

3 | ||

4 | A2 + T1 | |

5 | ||

6 | A3 | |

7 | T2 | |

8 | A4 | |

9 | ||

10 | A5 | |

11 | T3 | |

12 |

## Schedule of Material

### Overview of Schedule

- Week 1-4: Limits and Differentiation
- Weeks 5-8: Applications of Differentiation
- Week 9-12: Integration

### Week by Week Schedule

- Week 0: Pre-Course
- OpenStax 2.1 A Preview of Calculus (?)

- Week 1: Functions
- OpenStax 1.1 Review of Functions
- 14, 15, 17, 19, 46, 47, 53, 55

- OpenStax 1.2 Basic Classes of Function
- 59, 61, 69, 73, 83, 85, 87, 91, 93, 95, 97

- OpenStax 1.1 Review of Functions
- Week 2: Limits
- OpenStax 2.2 The Limit of a Function
- 35, 36, 37, 46, 47, 48, 59, 60, 61, 62, 63, 64

- OpenStax 2.3 The Limit Laws
- 83, 85, 93, 95, 111, 113

- OpenStax 2.2 The Limit of a Function
- Week 3: Differentiation
- OpenStax 3.1 Defining the Derivative
- 11, 13, 19, 25, 27, 39

- OpenStax 3.2 The Derivative as a Function (differentials!)
- 57, 59, 61, 65, 71, 73, 93

- OpenStax 3.1 Defining the Derivative
- Week 4: Differentiation
- OpenStax 3.3 Differentiation Rules
- 107, 111, 117, 123, 125, 127, 131

- OpenStax 3.5 Derivatives of Trigonometric Functions
- 175, 181, 183, 191, 193, 209

- OpenStax 3.3 Differentiation Rules
- Week 5: Related Rates
- OpenStax 3.6 The Chain Rule
- 215, 217, 221, 223, 235

- OpenStax 3.8 Implicit Differentiation
- 301, 303, 307

- OpenStax 4.1 Related Rates
- 1, 3, 5, 9, 17

- OpenStax 3.6 The Chain Rule
- Week 6: Optimization
- OpenStax 4.3 Maxima and Minima
- 91, 93, 95, 105, 107, 109, 117, 119, 123, 125, 129, 145

- OpenStax 4.7 Applied Optimization Problems
- 311, 317, 319, 321, 353

- OpenStax 4.3 Maxima and Minima
- Week 7: Curve Sketching
- OpenStax 4.5 Derivatives and the Shape of a Graph
- Additional Resource: log-log and semi-log graphs

- Week 8: Approximation
- OpenStax 4.2 Linear Approximations and Differentials

- Week 9: Antiderivatives and The Fundamental Theorem
- OpenStax 4.10 Antiderivatives
- OpenStax 5.3 The Fundamental Theorem of Calculus

- Week 10: Integration Techniques
- OpenStax 5.4 Integration Formulas and the Net Change Theorem
- OpenStax 5.5 Substitution

- Week 11: Area and Volume
- OpenStax 6.1 Areas between Curves
- OpenStax 6.2 Determining Volume by Slicing

- Week 12: Summary and Exam Prep

## Old Schedule

This is the old schedule from when I taught the course back in 2016. The following weekly
schedule uses section titles adapted from: Bittinger, Marvin L., Neal E. Brand,
and John Quintanilla. *Calculus for the life sciences.* 2006. As this syllabus
develops, I’ll add links to more recent resources.

- Functions and graphs
- Slope and Linear Functions
- Polynomial Functions
- Rational and Radical Functions

- Functions and graphs
- Trigonometric Functions
- Trigonometric Functions and the Unit Circle

- Differentiation
- Limits and Continuity: Visually and Numerically
- Limits and Continuity: Algebraically
- Differentiation as a Limit

- Differentiation
- Differentiation Techniques
- Instantaneous Rates of Change
- Product and Quotient Rules
- The Chain Rule
- Higher-Order Derivatives

- Applications of Differentiation
- Using the First Derivative to Find Max and Min
- Using the First Derivative to Sketch Graphs
- Using the Second Derivative to Find Max and Min
- Using the Second Derivative to Sketch Graphs

- Reading Week!
- Applications of Differentiation
- Graph Sketching: Asymptotes and Rational Functions
- Using Derivatives to Find Absolute Max and Min Values
- Maximum-Minimum Problems

- Applications of Differentiation
- Approximation Techniques
- Implicit Differentiation and Related Rates

- Explonential and Logarithmic Functions
- (!) Log-Log and Semi-Log Plots
- Exponential Functions
- Logarithmic Functions
- The Uninhibited Growth Model $\displaystyle \frac{dP}{dt} = kP$

- Explonential and Logarithmic Functions
- Decay
- The Derivatives of $a^x$ and $\log_a(x)$

- Integration
- Integration
- Area and Accumulation
- The Fundamental Theorem of Calculus

- Integration
- The Properties of Definite Integrals
- Substitution

- Integration
- Integration by Parts
- Tables and Technology
- Volume