### MAC2311:
Calculus and Analytic Geometry I

Instructor: Carlos Sotuyo

APEX Calculus: file - link

Univ of Wisconsin, Notes: file - link

Activities

**8/25** Intro to the course**: **Syllabus. Pearson Homework assignments. **
**2.1: Rates of Change and Tangent Lines to Curves. Notes 01.

Practice 01 [Students work in groups]

**8/27**

2.2: Limits of Functions and Limit Laws. Notes 02.

Practice 02.

**9/1**

2.3: The Precise Definition of a Limit

Practice 03 and 2.3 HW_questions to be discussed in class.

**9/3**

2.4: One-Sided Limits; 2.5: Continuity

Practice 04

**9/8**

2.6: Limits Involving Infinity; Asymptotes of Graphs.

Limits at Infinity, prof. Kouba, Univ of California at Davis: Q&A.

Practice 05

**9/10**

Review 01

**9/15**

**Test 1**

**9/17
** 3.1: Tangent Lines and the Derivative at a Point

3.2: The Derivative as a Function

Practice 06.

**9/22**

3.3: Differentiation Rules

3.4: Derivative as a Rate of Change. Particles' motion (1 page).

Practice 07. Particles' motion. Questions and answers.

**Question 1:**The curve y=ax^2+bx+c passes through the point (1,8) and is tangent to the line y=6x at the origin. Find a, b and c.

**Answer**here.

**Question 2**: A body moves on a coordinate line such that it has a position

s(t)=t^2 -5t+4 on the interval [0,6] in meters and t in seconds (...).

**Answer**here.

** 9/24
**3.5: Derivatives of Trig Functions

Practice 08

**9/29**

3.6: Chain Rule

Practice 09

**10/1**

3.7: Implicit Differentiation

Practice 10

**10/6**

3.8: Derivatives of Inverse Functions and Logarithms

Practice 11

**10/8**

3.9: Inverse Trigonometric Functions

Practice 12

**10/13**

3.10: Related Rates. Practice 13.

math.libretexts.org: related rates examples.

**10/15**

3.11: Linearization and Differentials. Practice 14.

**10/20**

Review 02.

**10/22**

**Test 2**

**10/27**

4.1: Extreme Values of Functions

4.2: The Mean Value Theorem

Practice 15

**10/29**

4.3: Monotonic Functions and the First Derivative Test.

Practice 16

**11/3**

4.4: Concavity and Curve Sketching

Practice 17

**11/5**

4.6: Applied Optimization

math.libretexts.org: optimization

Practice 18

**11/10**

4.8: Antiderivatives

Integration of x^n - Fermat's proof

Practice 19

**11/12**

Review 3 Chapter 4

**11/13**

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

Practice 20

**11/19**

5.3 The Definite Integral. Practice 21

Properties of definite integrals by mathopenref

**11/24**

5.4 The Fundamental Theorem of Calculus

5.5: Indefinite Integrals and the Substitution Method

Practice 22

**12/1**

5.6: Definite Integral Substitutions

7.1: The Logarithm Defined as an Integral

The logarithm defined as an integral by LibreText, UC Davis

Practice 23

**12/3**

Review 3

**12/8**

Test 3

Test 3

**12/10**

Final Exam Review

**12/15**

**Final Exam**