Ma 141 section 3 summer session II Homepage

Useful Materials and Links:

Course Sylabus ( grading scheme office hours etc...)

Course Schedule ( homeworks assigned and test dates )

MAPLE (required, all you need to know is online )

Additionally there are several optional help-sessions in Harrelson G-108
Thursdays: 11:30 am - 1:30 pm
Fridays: 10:00 am - noon and 3:00 - 5:00 pm


Tests with Solutions:

Test one solution

Test two solution

Test three solution

Course Lecture Notes:
Posted below are links to my lecture notes. Tests and quizzes will be given primarily on the basis of the material we discuss in these notes and your homework.

Basics of functions:

Review of functions, their properties, and graphs. We will use these ideas thoughout the course.

Motivations and limits:

Need for derivative, finite limits, and limits involving infinity.

Tangents and the derivative:

Definition of tangent to curve, definition of derivative at a point, and the derivative as a function. Finally, the derivatives of the basic functions are calculated.

Differentiation:

Having established all the basic derivatives we learn how to differentiate most any function you can think of. This is accomplished through the application of several rules and techniques: product rule, quotient rule, chain rule, implicit differentiation, logarithmic differentiation. These calculational tools form the heart of this course.

Parametrized curves and more:

Parametric curves discussed, Approximation of a function by the "best linear approximation" explained, finally a number of related rates problems worked out.

L'Hopital's Rule:

We return to the study of limits again. With the help of differentiation we are able to calculate many new limits through L'hopital's Rule. We discuss a number of different indeterminant forms and see how to determine each.

Graphing:

We study local and global maxima and minima of functions. A number of geometric ideas are introduced, increasing, decreasing, concave up, concave down, critical points, inflection points, local maximum, local minimum, absolute(global) maximum, absolute(global) minimum. These ideas are studied through the revealing and powerful lense of calculus. The first and sencond derivative tests are presented and applied to some examples.

Optimization:

We apply differential calculus to a number of interesting problems. The first and second derivative tests are applied to some real-life problems.

Basic Integration:

We define the definite integral and see how it gives the "signed" area under a curve. While it is intuitively clear that the definite integral defined by the limit of the Riemann sum gives the area under a curve, it is almost impossible to directly calculate that limit for most examples. Fortunately, we find that the fundamental theorem of calculus (FTC) allows us to avoid the messy infinite limit. Instead of finding the limit of the Riemann sum we merely must find the antiderivative of the integrand and use the FTC. Finding antiderivatives (aka indefinite integration) is a nontrivial task in general, we only begin the study listing the obvious examples from the basis of our study of differentiation. Then, we conclude our study by considering the technique of U-substitution. U-substitution is the most useful technique of integration, it is basically the analogue of the chain rule for integration.

More study helps: I may post things here as the course goes on.
Old Test #1 with solution from Fall 2004
Old Sample Test #2 solution from summer 2004
Old Test #2 from Fall 2004
Old Test #2 Solution from Fall 2004
Old Test #3 Solution from Fall 2004
Old Test #4 Solution from Fall 2004
Final from summer 2004
Practice test three from summer 2005 (NOW)
Extra Chain Rule Practice Problems and Solutions
Bonus Project (2pts)
GRADES


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Last Modified: 7-18-05