Math 1a (Section 1)
 
Freshman Mathematics
Fall 2014-15
 
MTWF 10:00 AM // 151 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Jay Williams, 256 Sloan, (626) 395-4338, jaywill@caltech.edu
Office Hours: 
Th 2-3 PM, F 11 AM-12 PM
Lead TA: Daiqi (Kevin) Linghu (626) 395-4366, dlinghu@caltech.edu
Office Hours: 
Sun 11 AM-12 PM



Feedback Form
Announcements
 




 



Course Description
  Top

Math 1a - Freshman Mathematics.

This course has two main goals:

  • Learning how to do explicit calculations
  • Discovering some fundamental mathematical properties, and in particular seeing some mathematical reasoning

Both of these goals are mostly focused on the basic analysis of integrals and derivations, and some famous functions such as trigonometric functions and the exponential function.

The following topics will be covered in this course:
  • Mathematical Induction
  • Completeness
  • Functions
  • Integral for Step Functions
  • Integral for More General Functions
  • Applications of Integration
  • Limits
  • Continuity
  • Intermediate Value Theorem
  • Inversion
  • Extreme - Value Theorem
  • Integrability Theorem
  • Mean - Value Theorem for Integrals
  • Derivatives
  • Implicit Differentiation
  • Extreme Values
  • Mean - Value Theorem for Derivatives
  • Curve Sketching
  • Fundamental Theorem of Calculus
  • Integration by Substitution
  • Integration by Parts
  • Logarithm
  • Exponential Function
  • Integration by Partial Fractions
  • Complex Numbers




Policies
  Top


Homework policies can be found here.

Textbooks
  Top


Text:
Calculus Volume 1, Tom M. Apostol ISBN 0-471-00005-1


Lecture Notes
  Top

Date Description

Course outline

Handouts
  Top

Date Description
Due Tues. Nov. 4 at 12 noon Midterm
Due Thurs. Dec. 11 at 12 noon Final

Homework
  Top

Due Date Homework  Solutions
Week 1 Tuesday, Wednesday, Friday Solutions
Week 2 Monday, Tuesday, Wednesday, Friday Solutions
Week 3 Monday, Tuesday, Wednesday, Friday Solutions
Week 4 Monday, Tuesday, Wednesday Solutions
Week 6 Monday, Tuesday, Wednesday, Friday Solutions
Week 7 Monday, Tuesday, Wednesday, Friday Solutions
Week 8 Week 8 Solutions
Weeks 9-10 Final week Solutions


  | © California Institute of Technology | Questions?  kaubry @ caltech.edu