Math131 Syllabus of Topics

Introduction: What is calculus?

Chapter 2: Limits and derivatives
2.1 The tangent and velocity problems
2.2 The limit of a function
2.3 Calculating limits using the limit laws
2.4 The precise definition of a limit
2.5 Continuity
2.6 Limits at infinity; horizontal asymptotes
2.7 Derivatives and rates of change
2.8 The derivative as a function

Chapter 3: Differentiation Rules
3.1 Derivatives of polynomials and exponential functions (see also 1.5)
3.2 The product and quotient rules
3.3 Derivatives of trigonometric functions
3.4 The chain rule
3.5 Implicit differentiation
3.6 Derivatives of logarithmic functions (see also 1.6)
3.7 Rates of change in the natural and social sciences
3.8 Exponential growth and decay
3.9 Related rates
3.10 Linear approximation and differentials

Chapter 4: Applications of Differentiation
4.1 Maximum and minimum values
4.2 The Mean Value Theorem
4.3 How derivatives affect the shape of a graph
4.4 Indeterminate forms and L'Hopital's Rule
4.7 Optimization problems
4.8 Newton's Method
4.9 Antiderivatives

Chapter 5: Integrals (introduction)
5.1 Areas and distances
5.2 The definite integral and Riemann sums