Math 1a Section 1
 
Freshman Mathematics
Fall 2011 - 12
 
MTWF 10:00, 151 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor: Andrei Jorza, 280 Sloan, 626-395-4839, ajorza@caltech.edu

Office Hours: Friday 3-4 pm

Lead TA: Tony Wong, 304 Kellogg, 626-395-4027, tonywong@caltech.edu

Office Hours: Saturday 8-9 pm

Recitation: Thursday 7:30 pm, Sloan 151

Course Secretary: Kathy Carreon, 253 Sloan, 626-395-4335, kcarreon@caltech.edu

 

Announcements
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October 12: The midterm will be due on October 31 at noon. There will be no homework due that day.
October 5: Andrei's office hours changed to Friday 3-4 pm.


Course Description
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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. .
  • Mathematical Induction
  • Sequences and Series
  • 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
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Homework

There will be weekly homework assignments. All assignments and due dates will be clearly posted in the Homework section below. Homework is due Monday at noon. Please submit your completed work in the appropriate Section Box outside of the Math Office, 253 Sloan. Graded assignments will be directly returned to you by your TA during office hours or at recitation. Late homework assignments will be accepted when accompanied with a note from the Dean or Health Center.

Exams

A two hour exam will be given after week 5 and a cumulative Final Exam. No one will be excused from the final. Only exams submitted in a Blue Book will be graded.

Grading

The awarding of a final grade of Pass or Fail will depend on a composite of these factors; the midterm exam will be worth 1/3, the final exam will be worth 1/3, and the homework will be worth 1/3. The lowest homework grade will be dropped.

Collaboration and Tools

The use of calculators, computer software, homework assignments and solution sets from previous terms, books and notes and or other such tools is NOT permitted on the exams. Collaboration on exams is not allowed.

Collaboration is allowed on the homework but you must write the solutions in your own words. Use of books and notes is allowed on the homework but you may not use solution sets from previous terms if they do the exact same problems. Use of calculators and computer software is allowed for homework but (unless software is specifically mentioned in the homework) only to check your work.

Recitations

Go to the recitations! Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA and bug him to death (figuratively speaking) with your questions, and try to fill in all the holes in your understanding of the subject. It is very important that you do not fall behind in class. Please seek help early and often when you have questions.

Extra Help

Tutoring is available for anyone who feels they would benefit from some extra assistance.

Do not hesitate to use the biggest teaching resource Caltech has to offer: its people. While asking solutions to homework (or exam) problems of others is not allowed (in contrast to collaborating on homework problems, where you look for a solution together with a fellow student), you are free to ask any question about the general theory to anyone. Some people you might want to ask questions to are: other students in the class, upperclassmen (in your house), the instructor and the TA. The best way to ask the instructor or the TA questions is to walk in at office hours, or to email questions, but you can also make an appointment.

Office Hours

Instructor and TA office hours can be found above.  

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

Lecture Notes
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Calculus Lecture Notes, by Dinakar Ramakrishnan

Topics Covered
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Date Description
September 26 Sets
September 27 Axioms of arithmetic
September 28 Axioms of the real numbers
September 30 Bounds and the real numbers
October 3 Real numbers contain square roots, mathematical induction
October 4 Complex numbers
October 5 Polar coordinates for complex numbers, what is a limit of a sequence
October 7 Limits of sequences of real and complex numbers, their uniqueness, and some examples
October 10 Properties of convergent sequences: sums, differences and ratios
October 11 Properties of convergent sequences: products and reciprocals
October 12 Properties of convergent sequences: inequalities and complex numbers. Monotonic sequences and convergence.
October 14 Examples of functions and properties of functions.
October 17 Continuous functions and limits of sequences; examples and counterexamples
October 18 Limits of functions and limits of sequences
October 19 Properties of limits of function. Continuity of trig functions.
October 21 Continuity of inverse functions, limits of trig functions
October 24 Examples of discontinuous functions and limits of trig functions.
October 25 Removable discontinuities; derivatives and examples.
October 26 Derivatives and algebraic operations
October 28 The chain rule and inverse functions
October 31 Log and exp
November 1 Continuous functions, intermediate value theorem and extremal values
November 2 Intermediate value theorem and why only the constant function has derivative 0
November 4 Finding extremal values with critical points and second derivatives
November 7 Exercises in extremal values
November 8 More exercises in extremal values
November 9 Basics of integration: Riemann sums
November 11 Integrals of x and x^s
November 14 Integrability of monotonic and continuous functions
November 15 Properties of integrals
November 16 The fundamental theorem of calculus and derivaties of integrals
November 18 Integration by parts
November 21 Change of variables
November 22 Computing some special integrals, and areas and volumes
November 23 Practice problems.
November 28 Taylor polynomials and estimates of errors
November 29 Linearization and examples of approximations
November 30 Tangents to curves described by equations or parametrically
December 2 Lengths of curves, and related rates of change

Homework
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Due Date Homework  Solutions
 October 10 @ 12 PM
  Homework 1
  Homework 1
 October 17 @ 12 PM  Homework 2
  Homework 2
 October 24 @ 12 PM  Homework 3
  Homework 3
 November 7 @ 12 PM  Homework 4  Homework 4
 November 14 @ 12 PM  Homework 5  Homework 5
 November 21 @ 12 PM  Homework 6  Homework 6
 December 2 @ 12 PM  Homework 7  

Exams
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Due Date Exam Type  Solutions
October 31 @ 12 PM Midterm Midterm
December 9 @ 12 PM Final Final

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