Math 11AB: Topics

Usual text for Math 11AB, Calculus with Applications:
BioCalculus: Calculus for Life Sciences by James Stewart and Troy Day.

Math 11A covers Chapters 1–4; Math 11B covers Chapters 5–7.

Gray sections are skipped and chapters not covered aren't shown.

WARNING: The text may be changed at the instructor's discretion.

1. Functions and Sequences

1.1 Four Ways to Represent a Function
1.2 A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Exponential Functions
1.5 Logarithms; Semi-log and Log-log Plots
1.6 Sequences and Difference Equations

2. Limits

2.1 Limits of Sequences
2.2 Limits of Functions at Infinity
2.3 Limits of Functions at Finite Numbers
2.4 Limits: Algebraic Methods
2.5 Continuity

3. Derivatives

3.1 Derivatives and Rates of Change
3.2 The Derivative as a Function
3.3 Basic Differentiation Formulas
3.4 The Product and Quotient Rules
3.5 The Chain Rule
3.6 Exponential Growth and Decay
3.7 Derivatives of the Logarithmic and Inverse Tangent Functions
3.8 Linear Approximations and Taylor Polynomials

4. Applications of Derivatives

4.1 Maximum and Minimum Values
4.2 How Derivatives Affect the Shape of a Graph
4.3 L’Hospital’s Rule: Comparing Rates of Growth
4.4 Optimization
4.5 Recursions: Equilibria and Stability
4.6 Antiderivatives

5. Integrals

5.1 Areas, Distances, and Pathogenesis
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 The Substitution Rule
5.5 Integration by Parts
5.6 Partial Fractions
5.7 Integration Using Tables and Computer Algebra Systems
5.8 Improper Integrals

6. Applications of Integrals

6.1 Areas Between Curves
6.2 Average Values
6.3 Further Applications to Biology
6.4 Volumes

7. Differential Equations

7.1 Modeling with Differential Equations
7.2 Phase Plots, Equilibria, and Stability
7.3 Direction Fields and Euler''s Method
7.4 Separable Equations
7.5 Systems of Differential Equations
7.6 Phase Plane Analysis

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