MTH 111 - Calculus 1 (differential Calculus)

MTH 111 Calculus 1 - Differential Calculus

Professor: Chaitanya Guttikar.

Office Hours:
Tuesdays: 12:20 PM to 1:20 PM.
Thursdays: 3:20 PM to 4:20 PM
Please inform me in the class or send me an email if you plan to visit my office hours.

Textbook: Essential Calculus by James Stewart.

Solutions to the latest Exam (Exam 2)!

Syllabus:
Short version: Chapters 1 through 4 of the textbook.

Long version:

Things you should already know (please revise using sections 1.1 and 1.2):

Functions and Their Representations:
Graphs, increasing/decreasing functions, one-to-one functions, composition of functions.
Standard functions:
Polynomial functions, rational functions, trigonometric functions, exponential and logarithmic functions. The compositions and graphs of all these functions.

The course aims to cover:

Limits and Continuity:
Limit of a function, left and right limits, continuous functions, the intermediate value theorem, techniques for calculating limits, ratios and compositions of continuous functions.
Derivatives:
Derivative of a function at a point, darivatives and rate of change, the geometric interpretation of derivative, derivative as a function, the mean value theorem for derivatives, techniques for calculating derivatives (product rule, quotient rule, chain rule etc), derivative and continuity, derivatives and shapes of graphs.
Applications of Derivatives:
Various applications of derivatives.
Definite Integrals:
The definition of definite integral, intermediate and mean value theorems revisited, The fundamental Theorem of Calculus, applications.

Assignments:

Due in class on Tuesday, Sept 8

Section 1.1: 2, 3, 10, 16, 20, 24, 26, 28, 32, 36, 38, 44, 48, 54.
Section 1.2: 2, 4, 12, 20, 24, 26, 34, 38, 44, 60, 62.

Due in class on Tuesday, Sept 15

Section 1.3: 2, 4, 8, 10, 24.
Section 1.4: 2, 4, 6, 10, 12, 18, 24, 34, 36, 38, 41, 44, 46, 54.

Due in class on Tuesday, Sept 22

Section 1.4: 30, 32, 40.
Section 1.5: 6, 8, 10, 14, 16, 20, 28, 30, 32, 34, 36, 38, 42, 46.
Section 1.6: 2, 4, 6, 8, 10, 14, 16, 20, 24, 26, 30, 38, 42.

Due in class on Thursday, October 22

Section 2.1: 4, 6, 10, 12, 14, 18, 22, 30, 34, 36, 40, 48.
Section 2.2: 2, 4, 6, 8, 10, 20, 22, 34, 40(a,b,c), 44.
Section 2.3: 2, 6, 10, 14, 16, 18, 22, 26, 32, 36, 40, 44, 48, 50, 58, 64, 68.
Section 2.4: 2, 6, 12, 16, 26, 28, 34, 36, 38, 40, 48, 50, 52.
Section 2.5: 2, 4, 10, 16, 24, 28, 34, 38, 40, 4852, 54, 58, 66.

Due in class on Thursday, October 22

Section 2.6: 2, 6, 8, 10, 14, 16, 18, 20 22, 24, 28, 32, 36, 38, 44.
Section 2.7: 4, 6, 8, 12, 16, 18, 20, 22, 26, 28, 30, 34, 38.
Section 2.8: 2, 12, 14, 16.
Homework Soltions Part 1, Part 2

Due in class on Tuesday, November 10

Section 3.1: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 34, 36, 40, 42, 44, 52, 54, 56, 58, 60.
Section 3.2: 2, 4, 6, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34.

Due in class on Thursday, November 19

Section 3.3: 2, 4, 6, 10, 12, 16, 22, 24, 28, 32, 36, 38, 42, 43, 46, 48.
Section 3.5: 2, 6, 8, 12, 16, 20, 24, 28, 30, 32, 44, 46, 48.