MAC2311 Calculus I


If you change the way you look at things, the things you look at change.
Max Plank

The real voyage of discovery consists not in seeking new landscapes, but in having new eyes.
Marcel Proust



MAC2311: Calculus I

This course includes topics in analytic geometry, limits, continuity, differentiation of algebraic and transcendental functions and their inverses, differentials, indeterminate forms and L’Hopital’s Rule, introduction to integration and the fundamental theorem of calculus, basic rules of integration and integration by substitution, and applications of definite integrals and derivatives. Certain sections of this course may require the use of a graphing calculator.

MAC2311: Activities

Fall 2019, Broward College


8/19 Intro to the course
2.1: Rates of Change and Tangent Lines to Curves
Practice 01

8/21
2.2: Limits of Functions and Limit Laws
2.3: The Precise Definition of a Limit
Practice 02 and 2.3 HW_questions to be discussed in class.

8/26
2.4: One-Sided Limits; 2.5: Continuity
Practice 03

8/28
2.6: Limits Involving Infinity; Asymptotes of Graphs.
Limits at Infinity, prof. Kouba, Univ of California at Davis: Q&A.
Practice 04.

9/4
Review 1

9/9
Test 1

9/11
3.1: Tangent Lines and the Derivative at a Point
3.2: The Derivative as a Function
Practice 05. Practice 05 handwritten answers.

9/16
3.3: Differentiation Rules
3.4: Derivative as a Rate of Change. Particle motion (1 page).
Practice 06. Worked answers to question 14 to 22.
Khan Academy Video: Interpreting change in speed from velocity-time graph.
Khan Academy Video: Motion problems: when a particle is speeding up.
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.

9/18
3.5: Derivatives of Trig Functions
Practice 07

9/23
3.6: Chain Rule
Practice 08

9/25
3.7: Implicit Differentiation
Practice 09 Correction to No.7 here. Worked answers, here.

9/30
3.8: Derivatives of Inverse Functions and Logarithms
Practice 10

10/02
3.9: Inverse Trigonometric Functions
Practice 11

10/09
3.10: Related Rates. Practice 12.
math.libretexts.org: related rates examples.

10/14
3.11: Linearization and Differentials. Practice 13HW questions pdf.

10/16
Review 2. Handwritten Ans to questions 27 to 32.

10/21
Test 2

10/23
4.1: Extreme Values of Functions
4.2: The Mean Value Theorem
Practice 14

10/28     
4.3: Monotonic Functions and the First Derivative Test.
4.4: Concavity and Curve Sketching
Practice 15

10/30
     
4.6: Applied Optimization
math.libretexts.org: optimization
Practice 16

11/4       
4.8: Antiderivatives. Practice 17

11/6       
Review 3 Chapter 4
Handwritten answers to Qns 19 to 30
(Answers to qns 1 thru 18 discussed in class on 11/6)

11/13     
5.1  Area and Estimating with Finite Sums
5.2  Sigma Notation and Limits of Finite Sums
Practice 18

11/18     
5.3  The Definite Integral. Practice 19
Properties of definite integrals by mathopenref

11/20     
5.4  The Fundamental Theorem of Calculus
5.5: Indefinite Integrals and the Substitution Method
Practice20

11/25
     
5.6: Definite Integral Substitutions
7.1: The Logarithm Defined as an Integral
The logarithm defined as an integral by LibreText, UC Davis
Practice21

11/27     
Review 3 Chapter 5

12/2       
Test 3


12/4       
Review Final Exam

12/9       
Final Exam

 


Broward College, South Campus.
Instructor: Carlos Sotuyo
email: csotuyo@broward.edu

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Syllabus_MAC2311: MW, 5:00 pm-7:20 pm
Building 70, Room 111
Office Hours: Building 69,
Room 237: 4:10 pm -4:50 pm, Mondays

HW Student registration handout


The most complete Calculus course:

Paul
Paul Online Notes
Paul Cheat Sheets

ppt

PPTs downloadable zip folder

utah
Calculus I Video Lectures


A Graphing calculator is highly recommended.
TI 84 or Casio 9750GII.  

casio

ti84

Millersville University:
final-review
sheets & solutions for Basic Algebra, Trigonometry, Calculus 1, 2 & 3 .

MATHISPOWER4U tutorials: Algebra, Calculus I, II, III, differentail eq, set theory, logic, etc.

List of derivatives rules from UCDavis.

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Single Variable Calculus
Prof. David Jerison

calc

Numberphile: Zero factorial: 0! = 1