Course Notes for Math 250A
Textbook
Larson and Edwards, Calculus, 11th edition
Week 1
Review of Limits and Continuity (sections 1,2, 1.3, 1.4, 1.5)
Review of Derivatives (sections 2.2, 2.3, 2.4)
Handout: Basic derivatives
Derivatives of Trig Functions (sections 2.3, 2.4)
Handout: Trigonometric formulas
Derivatives of Exponentials and Logs (sections 5.1, 5.4)
Week 2
Section 5.7 Inverse Trigonometric Functions: Differentiation
Handout: Inverse trig functions
Examples: Application problems
Proof of Inverse Trig Derivatives
Section 2.5 Implicit Differentiation
Review of Integration (sections 4.4, 4.5, 5.2)
Handout: Fundamental Theorem of Calculus
Section 5.8 Inverse Trigonometric Functions: Integration
Section 5.9 Hyperbolic Functions (This section will not be tested.)
Week 3
Section 8.1 Basic Integration Rules
Handout: Basic Integration Formulas
Section 8.2 Integration by Parts
Handout: Integration by Parts
Handout: Tabular method examples
Section 8.3 Trigonometric Integrals
Week 4
Section 8.4 Trigonometric Substitution
Handout: Trigonometric Substitution
Section 8.5 Partial Fractions
Example: Quadratic denominator
Example: What method to use?
Handout: Partial Fractions
Week 5
Section 5.6 Indeterminate Forms and L'Hôpital's Rule
Handout: Indeterminate forms of limits
Section 8.8 Improper Integrals
We will now move to chapter 10. We will cover chapter 9 later this semester.
Section 10.1 Conics and Calculus
Week 6
Section 10.2 Plane Curves and Parametric Equations
Desmos graph of a parametric curve
External link: Cycloid
Section 10.3 Parametric Equations and Calculus
Arc Length and Surfaces of Revolution
Week 7
There are no notes for week 7, it is the reading break.
Week 8
Section 10.4 Polar Coordinates and Polar Graphs
Handout: Polar graphs examples
Section 10.5 Area and Arc Length in Polar Coordinates
External link: Area in Polar Coordinates
Week 9
Section 9.1 Sequences
Section 9.2 Series and Convergence
Section 9.3 The Integral Test and p-Series.
Handout: Harmonic series
Section 9.4 Comparisons of Series
Week 10
Section 9.5 Alternating Series
Section 9.6 The Ratio and Root Tests
Handout: Summary of tests for series
Section 9.7 Taylor Polynomials and Approximations
Week 11
Section 9.8 Power Series
External link: Power Series
Section 9.9 Representation of Functions by Power Series
Example: An integral with series
Section 9.10 Taylor and Maclaurin Series
Handout: Maclaurin series of sin(x)
Handout: Basic Maclaurin series
Week 12
Section 12.1 Vector-Valued Functions
Section 12.2 Derivatives and Integrals of Vector Functions
Week 13
Section 12.3 Velocity and Acceleration
Section 12.4 Tangent and Normal Vectors
Week 14
Section 12.5 Arc Length