## Calculus I

### MAT 131

#### Spring 2009

Mathematics department
Julia Viro

Instructors Schedule Assignments Exams Generalities Help

## Tentative schedule

Week of Contents Sections
1/26-1/30 Functions and their graphs. Domain, range. Even and odd functions, increasing and decreasing functions. Operations on functions: sum, difference, product, quotient, composition. Elementary vs nonelementary functions. 1.2, 1.3
2/2-2/6 Basic elementary functions: linear functions, polynomials, rational, power, trigonometric and exponential functions. Inverse functions. Logarithm. Inverse trigonometric functions: arcsine, arccosine, arctangent. 1.2, 1.5, 1.6
2/9-2/13 The limit of a function. Limit laws. Continuity. Types of discontinuity. Squeeze theorem. Intermediate value theorem. Limits involving infinity. Vertical, horizontal and oblique asymptotes. Calculating technique for limits. 2.1-2.5
2/16-2/20 The derivative of a function and its geometrical meaning. Tangent line. Derivative as velocity. Linearization. Derivatives of higher orders. Derivatives and shapes of curves. 2.6-2.8, 3.8, 4.2-4.3
2/23-2/27 Review for Midterm I. Midterm I is on Wednesday 2/25 at 8:30-10:00pm
3/2-3/6 Differentiation laws. Chain rule. Derivative of inverse function. Derivatives of elementary functions. Differentiation technique. 3.1-3.5
3/9-3/13 Implicit differentiation. Parametric curves. Related rates problems. 3.6-3.7, 1.7, 4.1
3/16-3/20 Review for Midterm II. Midterm II is on Monday 3/23 at 8:30-10:00pm
3/23-3/27 Rolle's, Lagrange's and Cauchy's theorems. Indefinite forms and L'Hopital's rule. 4.3, 4.5
3/30-4/3 Graphing. 4.2, 4.4
4/6-4/10Spring recess
4/13-4/17 Extreme Value Theorem. Optimization problems. Antiderivative and indefinite integral. 4.2, 4.6, 4.9
4/20-4/24 Definite integral and its properties. Definite integral as limit of Riemann sums. 5.1-5.2
4/27-5/1 The Fundamental Theorem of Calculus. Integration by substitution. 5.3-5.5
5/4-5/8 Review for Final.
Friday 5/15
8:00-10:30am
Final exam