Student Body:

This course is intended for Honors students and it is open to freshmen.

Background and Goals:

Topics in first semester calculus. Enroll Info: This is the first semester of the calculus honors sequence. Course is available by invitation only for freshmen students who placed into MATH 221.

Alternatives:

Math 221-222.

Subsequent Courses:

Math 276

Course Content:

- Introduction
- Real numbers and the completeness axiom
- Mathematical induction
- Some inequalities

- Integral Calculus
- Functions
- Area as a set function and step functions
- Integrals of step functions
- Integrals of general functions
- Integrals of monotonic functions
- Integrals of powers and polynomials
- Properties of the integral

- Applications of Integration
- Area between two graphs
- Integrating trig functions
- Integrals in polar coordinates
- Calculation of volume
- Work and average value
- Indefinite integrals

- Continuous Functions
- Limits of functions
- Continuity
- Properties of limits
- Composite functions and continuity
- Intermediate value theorem
- Inverse functions and their properties
- Extrema and uniform continuity
- Integrability of continuous functions

- Differential Calculus
- Differentiating a function
- Algebra of derivatives
- The derivative as a slope
- The chain rule
- Applications of the chain rule
- Extreme values of functions
- The mean value theorem
- First and second derivative tests
- Curve sketching

- Integration and Differentiation
- The derivative of an indefinite integral
- Primitive functions
- Integration by substitution
- Integration by parts

- The Logarithm, The Exponential, and Inverse Trigonometric Functions
- Definition of logarithm as an integral
- Differentiation and integration formulas
- The exponential function
- Differentiation and integration formulas
- Inverse trigonometric functions

credits:

5 (r-N-I)

semester:

Fall

prereqs:

Consent of instructor.