In this page, I post the notes and the material you need to know for each class (before and after the class!) For each lecture, the textbook section corresponding to that lecture is also posted. For example: Limits: Section 1.1 & 1.2

Final Exam Review Material

Review Notes Ignore questions 4,15,22,29 of the optimization section.
Solutions to selected problems of the review note.
Solutions to optimization questions
Short Questions: (updated) True/False, multiple choice
Solutions to short questions

* Week 13: Taylor Polynomial and Anti-derivative

Additional Topics: Two topics you need to know if you are taking the Integral Calculus course. Not part of our exam.
Lecture 35: Anti-derivative
Lecture 34: Higher degree approximation (Taylor Polynomial)

* Week 12: Approximation

Lecture 33: Quadratic Approximation vs Linear Approximation
Lecture 32: Linear Approximation

* Week 11: More on Optimization

worksheet: more samples of optimization problems (there are lots of them on WebWork.)
Lecture 31: Optimization with parameters (Q9 of the worksheet)
Lecture 30: Solving Questions 4 and 3 of the worksheet. Complete solution  to Q3 of the worksheet.
Lecture 29: Complete the worksheet from last week and question 1 from the other worksheet.

* Week 10: Optimization (Good to attend the class for this topic.)

worksheet: Steps in solving an optimization problem & a step-by-step example
Lecture 28: Optimization (completing the examples from last class.)
Lecture 27: Optimization: Examples
Lecture 26: Global Extrema: Graphical and computational.

* Week 9: Curve sketching

Curve Sketching Practice, from UCDavis online notes.
Lecture 25: A warm-up curve sketching exercise before the quiz.
Lecture 24: Sketching the curve of another rational function and an exponential function.
Lecture 23: Sketching the curve of a rational function.

* Week 8: l’Hopital’s Rule

Lecture 22: One l’Hopital example and Curve Sketching. Solution to the curve sketching exercise in the note.
Lecture 21: Other forms of indeterminate limits: inf-inf , 0 * inf. Solution to limit exercises in the note.
Review Hand-out, Solution to solved problems in the review session
Lecture 20  l’Hopital’s rule to find 0/0 and inf/inf limits.

* W Reading Week 😉

* Week 7: Vertical and Horizontal Asymptotes of the function

Lecture 19: Asymptotic behavior of a function: Horizontal Asymptote
Lecture 18: Asymptotic behavior of a function: Vertical Asymptote

* Week 6: Concavity of the function f and its relation with the second derivative f”: S3.4

Quick Test: Graphical interpretation of f’ and f”. Solution
Lecture 17: Strategies in computations of f’, f”, critical numbers, etc.
Lecture 16: Examples of sign charts for f’ and f”
Lecture 15: Concavity of f and the sign of f”

* Week 5: Increasing/Decreasing function and the 1st derivative test: S3.3

Lecture 13&14 + practice problems: Examples on finding the local extrma using the 1st derivative test. Intervals of increase and decrease in f.
Lecture 12: Finding intervals of increase/decrease of a function using its derivative, 1st derivative test to find local extrema.
Quick Test 3 (with solution)
Quick Test 2 ,  Solution
Quick Test 1 (with solution)

Check out the following tutorials from Paul’s Online Math Notes on working with inequalities to determine the sign of expressions: Tutorial 1: Polynomials Tutorial 2: Rational functions

* Week 4: Local extrema, critical numbers, Mean Value Theorem: S3.1 & 3.2

Trapezoidal Tank: Follow these steps to solve the WebWork 2.4 problem.
Lecture 11: Mean Value Theorem, Rolle’s Theorem, application and examples
Lecture 10: More examples on finding critical numbers.
Worksheet 4: Intro to Mean Value Theorem. Solution to worksheet 4.
Lecture 9: Local max/min and critical numbers (concept, definition, examples)

* Week 3: Related Rates Cont’d

In class Worksheet 3. Solution to worksheet 3.
In class Worksheet 2. Solution to worksheet 2.

* Week 2: Implicit differentiation cont’d & Related rates: S2.6

Lecture 4&5: Introduction to related rates word problems and the strategies to solve a typical related rates problem.
In class Worksheet 1. Solution to worksheet 1.
Lecture 3: Finding the second derivative of an implicit curve. Solve the practice problems at the end of the notes. Solution to practice problems of this lecture.

* Week 1: Implicit Differentiation: S2.9

Lecture 2: Implicit differentiation, the tangent line to an implicit curve.
Lecture 1: Review of the chain rule, introduction to implicit curves.