Accelerated Calculus

Math 1450H

Fall 2014

L 212S, TuTh 2:30-4pm

 

Instructor   

Bernhard Bodmann, Send Email

Office

Mo, We 1:30-2:30pm, 604 PGH, (ph) 713 743 3581

Textbook

Calculus, Early Transcendentals (6th edition), by James Stewart (2008) ISBN 0-495-01166-5 (old edition, less expensive than current one, beware of non-identical books with similar titles!)

Course website

www.math.uh.edu/~bgb/Courses

Course objective 

This is the first course of a two-semester sequence covering all major Calculus content. The main goals of this course are to

Preparation, Homework, Quizzes and Exams

This is a fast paced course. You are required to read the sections covered each week during the weekend before and begin to familiarize yourself with the posted problems. Selected problems will then be worked out in the recitation sections. In addition, you may consult the solutions key at the end of the book to check your answers. At the end of each week, you are responsible for knowing how to solve all posted homework problems! On most Fridays, the material of the week will be tested with an 18-minute quiz in the lab session. Groups of two chapters usually make up the material for each in-class exam. The final exam is comprehensive, with a slight emphasis of the material of the last two weeks.

Grading

Your total score is composed of exam and quiz scores

 3 x 200 pt. exams  600 points 
 10 x 30 pt. quizzes  270 points (drop lowest score)
 Final exam  330 points

 TOTAL

 1200 points 

Final grades will be based on the total of 1200 points. You are guaranteed a grade based on the standard scale, that is:  A >=9O% > B >=8O% > C >= 7O% > D >= 6O% > F. However, I will adjust the scale downward in case the distribution of scores indicates that I should. Attendance is mandatory, so apart from dropping the lowest quiz score any missed quiz counts as zero. Documented medical or University of Houston excused absences will be permitted, in which case your score will be prorated accordingly.

Disabilities

Whenever possible, and in accordance with 504/ADA guidelines, we will attempt to provide reasonable academic accommodations to students who request and require them.

Getting help

Free tutoring is available at CASA. Tutors are usually available Mo-Th 9am-7pm, Fr 9am-2pm.

Material (numbering follows chapters in the textbook)

LIMITS AND CONTINUITY (2 lectures)

2.3 Calculating limits
2.4 The definition of a limit
2.5 Continuity

DERIVATIVES (6 lectures)

3.1 Derivatives of elementary functions
3.2 Product and quotient rules
3.3 Derivatives of trigonometric functions
3.4 The chain rule
3.5 Implicit differentiation
4.4 L'Hospital's rule
3.7 Derivatives of logarithmic functions
3.8 Exponential growth and decay
3.9 Related rates

APPLICATIONS OF DIFFERENTIATION (2 lectures)

4.1 Maximum and minimum values
4.2 The Mean Value Theorem
4.3 Derivatives and the graph of functions
4.7 Optimization problems

INTEGRALS (2 lectures)

5.1 Maximum and minimum values
5.2 The Mean Value Theorem
5.3 Derivatives and the graph of functions
5.4 Optimization problems
5.5 The substitution rule

TECHNIQUES OF INTEGRATION (4 lectures)

7.1 Integration by parts
7.2 Powers and products of trigonometric functions
7.3 Trigonometric substitutions
7.4 Partial fractions: linear factors
7.5 General strategies for integration
7.8 Improper integrals

APPLICATIONS OF INTEGRATION (3 lectures)

6.1 Areas between curves
6.2-6.3 Volumes by slices and solids of revolution
8.1 Arc length
8.2 Area of Surfaces of Revolution

INFINITE SEQUENCES and SERIES (5 lectures)

11.1 Sequences
11.2 Infinite Series: Fundamentals and the Geometric Series
11.3 The Integral Test
11.4 Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence, the Ratio and Root Tests
11.7 Strategy for testing series

POWER SERIES and TAYLOR EXPANSIONS (2 lectures)

11.8 Power Series and Their Regions of Convergence
11.9 Representation of Functions as Power Series, Calculus of Power Series
11.10 Taylor and MacLaurin Series, Uniqueness of Power Series