MATH 141- Calculus I

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MATH 141- Calculus I 

Course Description:

Functions, limits, derivatives, introduction to integrals, the Fundamental Theorem of Calculus, applications of derivatives and integrals
Prerequisites: placement code MA4-9 or MD0-9 required; earned by grade of C or better in MATH 112. 115, 116, or by Precalculus Placement Test

SAMPLE COURSE OVERVIEW

For most students, Calculus I is the first serious contact with Mathematics. The core of Calculus I is the understanding of Derivatives and Integrals. We will also study the graphs of functions as the main application of the above. The nature of this course requires more the understanding of the above notions rather than memorizations of formulas. Throughout the history, the study of these notions and ideas was fundamental and necessary for the development of Mathematics, Physics and Mechanics. Some of the main contributors were Eudoxus (400-347) , Archimedes (287-212), Leibniz (1646-1716), Euler (1707-1783), Cauchy (1789-1857), Riemann (1826-1866).

ITEMIZED LEARNING OUTCOMES

Upon successful completion of Math 141, students will be able to:
1. Demonstrate understanding of the following concepts: Limits and Continuity of Functions, The Derivative, Applications of the Derivative: Study of Graphs, Minima-Maxima, Mean Value Theorem, The Integral, The Fundamental Theorems of Calculus\
2. Compute derivatives and basic integrals
3. Apply these concepts to modeling real life problems at the usual level of first semester calculus.

SAMPLE REQUIRED TEXTS/SUGGESTED READINGS/MATERIALS

1. Calculus Early Transcendentals, James Stewart, 6E

SAMPLE ASSIGNMENTS AND/OR EXAM

1. Homework
a. Homework will be assigned regularly (on BlackBoard) but will not be graded. However, it is very important that you do the homework as soon as we cover the appropriate material, since otherwise you will not be able to solve problems yourself and consequently will not do well on quizzes and tests.
2. Quizzes
a. Quizzes will be given regularly and unannounced, both in the lectures and in the recitations.

3. Midterm Exams: 3 midterm exams

4. Final Exam: The final exam will be cumulative.

SAMPLE COURSE OUTLINE WITH TIMELINE OF TOPICS, READINGS/ASSIGNMENTS, EXAMS/PROJECTS

Class 1:
 1.1

Intro to calculus;



Functions: the Rule of Four
Class 2:
 1.2, 1.3
 A Catalog of Essential Functions; New Functions from Old
Class 3:
 1.4, 1.5
 Exponential and Logarithmic Functions
Class 4:
 2.1
 The Tangent and Velocity Problems
Class 5:
 2.2, 2.3
 The Limit of a Function; Calculating Limits
Class 6:
 2.4
 Definition of Limit; Continuity

2.5
Class 7:
2.6
 Limits at Infinity; Horizontal Asymptotes
Class 8:
 2.7
 Derivatives and Rates of Change
Class 9:
 2.8 
 Derivative as a Function
Class 10:
 Review
Class 11:
 Exam 1
Class 12:
 3.1
 Derivatives of Polynomials and Exponential Functions
Class 13:
 L3.2
 Product and Quotient Rules
Class 14:
 3.3
 Derivatives of Trig Functions
Class 15:
 3.4 Chain Rule
Class 16:
 3.5
 Implicit Differentiation
Class 17:
 3.6
 Derivatives of Log Functions
Class 18:
Differentiation Rules: summary and Additional Practice
Class 19:
 3.9
 Related Rates
Class 20:
 4.1
 Max and Min Values
Class 21:
 4.2
 Mean Value Theorem
Class 22:
  4.3
 Derivatives and the Shape of a Graph
Class 23:
 4.4
 Indeterminate Forms and L'Hospital Rule
Class 24:
 4.4
 Indeterminate Forms; Curve Sketching
Class 25:
 4.5
Summary of Curve Sketching
Class 26:
 Review
  
Class 27:
 Exam2
  
Class 28:
 4.7
 Optimization Problems
Class 29:
 4.7
 Optimization Problems
Class 30:
 4.9
 Antiderivatives
Class31:
 5.1
 Areas and Distances
Class 32:
 5.2
The Definite Integral
Class 33:
 5.3
 The Fundamental Theorems of Calculus
Class 34:
 5.4
 Indefinite Integrals and the Net Change Theorem
Class 35:
 5.5
 The Substitution Rule
Class 36:
 5.5
 More on Substitution,

6.1
 Intro to Area between Curves
Class 37:
 6.1
Areas between Curves
Class 38: 
 Review
Class 39:
 Exam 3
Class 40:
 6.2
 Volumes: Disks and Washers
Class 41:
6.2
Review
More on Volume





Class 42:
 Review
FINAL EXAM
Final Exam according to University exam schedule

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