### MAC2311:
Calculus and Analytic Geometry I

Instructor: Carlos Sotuyo

APEX Calculus: file - link

Univ of Wisconsin, Notes: file - link

Activities

**8/24** 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] Practice 01 Ans

**8/26**

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

Practice 02. [Students work in groups] Practice 02 Ans

HW qns on limits | Answers

**8/31**

2.3: The Precise Definition of a Limit. Notes 03. Notes on Absolute values (review).

Practice 03 [Students work in groups] Practice 03 Ans

2.3 HW_questions to be discussed in class. Step by Step Slns.

LibreTexts Epsilon-Delta definition of limit at UCDavis.

**9/2**

2.4: One-Sided Limits; 2.5: Continuity. Notes 04.

Practice 04 [Students work in groups] Practice 04 Ans

**9/9**

2.6: Limits Involving Infinity; Asymptotes of Graphs. Notes 05.

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

Practice 05 [Students work in groups] Practice 05 Ans

**9/14**

Review 01 | Review 01 handwritten notes.

Two limits (examples)

**9/16**

**Test 1**

**9/21
** 3.1: Tangent Lines and the Derivative at a Point.

3.2: The Derivative as a Function. Notes 06.

Practice 06 [Students work in groups] Practice 06 Ans.

**9/23**

3.3: Differentiation Rules

3.4: Derivative as a Rate of Change. Particles' motion (1 page). Notes 07.

Particles' motion: Questions and answers. || The Physics Hypertextbook.

**Question 1:**The curve y=ax^2+bx+c passes through (...)

**Question and Answer**here.

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

s(t)=t^2 -5t+4 (...).

**Question and**

**Answer**here.

Practice 07 [Students work in groups] Practice 07 Ans.

**9/28**

3.5: Derivatives of Trig Functions. Notes 08.

Practice 08 | [Students work in groups] |Practice 08 Ans.

**9/30**

3.6: Chain Rule. Notes 09.

Practice 09 | [Students work in groups] Practice 09 Ans.

3.7: Implicit Differentiation. Notes 10.

Practice 10 | [Students work in groups] |Practice 10 Ans

**10/5**

3.8: Derivatives of Inverse Functions and Logarithms

Practice 11 | [Students work in groups] |Practice 11 Ans

**10/7**

3.9: Inverse Trigonometric Functions

Practice 12 | [Students work in groups] |Practice 12 Ans

**10/12**

3.10: Related Rates.

Practice 13 | [Students work in groups] |Practice 13 Ans

math.libretexts.org: related rates examples.

3.11: Linearization and Differentials.

Practice 14 | [Students work in groups] |Practice 14 Ans

**10/14**

Review 02.

**10/19**

**Test 2**

**10/21**

4.1: Extreme Values of Functions

4.2: The Mean Value Theorem

Practice 15 | [Students work in groups] |Practice 15 Ans

**10/26**

4.3: Monotonic Functions and the First Derivative Test.

Practice 16 | [Students work in groups] |Practice 16 Ans

**10/28**

4.4: Concavity and Curve Sketching

Practice 17 | [Students work in groups] |Practice 17 Ans

**11/2**

4.6: Applied Optimization

math.libretexts.org: optimization

Practice 18

**11/4**

4.8: Antiderivatives

Integration of x^n - Fermat's proof

Practice 19

**11/9**

Review 3 Chapter 4

**11/16**

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

Practice 20

**11/18**

5.3 The Definite Integral. Practice 21

Properties of definite integrals by mathopenref

**11/23**

5.4 The Fundamental Theorem of Calculus

5.5: Indefinite Integrals and the Substitution Method

Practice 22

**11/30**

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

**12/2**

Review 7

Test 3

Test 3

**12/9**

Final Exam Review

**12/14**

**Final Exam**