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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
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