### MAC2311:
Calculus and Analytic Geometry I

Fall of 2020. 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. [Students work in groups]

HW qns on limits | To be discussed in class.

**9/1**

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

Practice 03 [Students work in groups]

2.3 HW_questions to be discussed in class.

LibreTexts Epsilon-Delta definition of limit at UCDavis.

**9/3**

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

Practice 04 [Students work in groups]

**9/8**

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]

**9/10**

Review 01

Two limits (examples)

**9/15**

**Test 1**

**9/17
** 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]

**9/22**

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]

**9/24**

3.5: Derivatives of Trig Function. Notes 08.

Practice 08 [Students work in groups]

**9/29**

3.6: Chain Rule. Notes 09.

Practice 09 [Students work in groups]

**10/1**

3.7: Implicit Differentiation. Notes 10.

Practice 10 [Students work in groups]

**10/6**

3.8: Derivatives of Inverse Functions and Logarithms. Notes 11.

Practice 11 [Students work in groups]

**10/8**

3.9: Inverse Trigonometric Functions. Notes 12.

Practice 12 [Students work in groups]

**10/13**

3.10: Related Rates. Notes 13.

Practice 13 [Students work in groups] Practice 13Ans

math.libretexts.org: related rates examples.

**10/15**

3.11: Linearization and Differentials. Notes 14.

Practice 14 [Students work in groups]

**10/20**

Review 02.

**10/22**

**Test 2**

**10/27**

4.1, 4.2: Extreme Values of Functions. The Mean Value Theorem. Notes 15.

Practice 15 [Students work in groups]

**10/29**

4.3: Monotonic Functions and the First Derivative Test. Notes 16.

Practice 16 [Students work in groups]

**11/3**

4.4: Concavity and Curve Sketching. Notes 17.

Practice 17 [Students work in groups]

**11/5**

4.6: Applied Optimization. Notes 18. Examples.

Setion 4.6 HW Qns

math.libretexts.org: optimization

Practice 18

**11/10**

4.8: Antiderivatives. Notes 19.

Integration of x^n - Fermat's proof

Practice 19

**11/12**

Review 3 Chapter 4

**11/17**

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums. Notes 20

Practice 20

**11/19**

5.3 The Definite Integral. Notes 21

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. Notes 22

Practice 22

**12/1**

5.6: Definite Integral Substitutions

7.1: The Logarithm Defined as an Integral. Notes 23

The logarithm defined as an integral by LibreText, UC Davis

Practice 23

**12/3**

Review 4 Chapter 5

**12/8**

Test 3

Test 3

**12/10**

Final Exam Review

**12/15**

**Final Exam**