** ----------------------------------------- **

** Ahmed Kaffel, PhD **

Department of Mathematical Sciences

University of Wisconsin-Milwaukee

College of Letters and Science

3200 N Cramer Street

Milwaukee, WI 53211-3029

**Office:** EMS Building, Room E434

**Tel:** (414) 629-1090

**E-mails: kaffel@uwm.edu / kaffel@vt.edu**

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The Concept of Functions

Essential Functions

Introduction to Limits

Computing with Limits, Limit Laws

The Precise Definition of Limits

Limits at Infinity

Continuity

Introduction to Derivatives

Derivatives as Functions

Derivatives of Basic Functions

Differentiation Rules

Derivatives of Trigonometric Functions

Implicit Differentiation

Logarithmic Differentiation

Related Rates

Exponential Growth and Decay

Linear Approximation and Differentials

Minima and Maxima

The Mean Value Theorem

Derivatives and the Shape of Graphs

L'Hospital's Rule

Curve Sketching

Using derivatives to analyze functions

Optimization

Introduction to Integrals

The Area Problem

The Definite Integral

The Fundamental Theorem of Calculus

The Indefinite Integral

The Area Between Curves

The Substitution Rule for Integration

The Average Value of Functions (the Mean Value Theorem for Integrals)

Some practice problems

- Practice-functions
- Practice-functions (Solutions)
- Functions and Quadratics Problems
- Functions and Quadratics Problems (Solutions)
- Exponent and logarithm rules
- Graph of a function
- Graph of a function (solution)
- Graphs Review
- Graphs and limits problems
- Graphs and limits problem solutions
- Limits, Continuity, and the Derivative Review
- Problems- Compound interest
- Derivative rules examples
- Derivative of exponential and ln(x)
- Derivative of exponential and ln(x) (solutions) Product Rule
- Problems- Product rule
- Problems- Product rule (solutions)
- Problems- quotient rule
- Problems- quotient rule (solutions)
- Problems- chain rule
- Problems- chain rule (solutions)
- Differentiation of Trigonometric Functions
- Differentiation of Trigonometric Functions (solutions)
- Problems: Analyzing functions
- First and second derivative tests
- Practice: Finding Area Between Curves
- Practice: Finding Area Between Curves
- Practice: Integral applications

Some Review Problems for the exams

- Function review
- Review derivative of a function
- Various problems with solutions> Math 211- Review problems for exam spring 2023 Math 211- Review problems for exam spring 2023
- Math 211- Review problems for exam spring 2023
- Math 211- Review problems for exam spring 2023
- Math 211- Final Exam Review Part 1 sp23
- Math 211- Final Exam Review Part 2 sp23