Syllabus | MATH 2413 400 - CALCULUS I

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TENTATIVE SCHEDULE

In Class Sections/Topics

Suggested Homework Exercises

Week 1

Diagnostic Test A

Calculus Overview

The Ideas of Calculus: Derivatives

Limits: Graphical Approach

Limits: Numerical Approach

Diagnostic Test B

The Ideas of Calculus: Integration

Limits: Analytic Approach

§2.1 (p.67): 6,7,9

§2.2 (pp.75-76): 2,4,6,10,14,16, 18,20,22,24,26,30

§2.3 (p.87): (4-40)x4, 42,(46-62)x2

Week 2

Diagnostic Test C

Introduction to Proof

Special Limits

Formal Definition of Limit

Properties of Limits

Strategy for Finding Limits

Diagnostic Test D

Continuity

One-Sided Limits

Intermediate Value Theorem

Infinite Limits

Limits at Infinity

§2.2 (p.76): 32,34,36,38,40,46,48,50

§2.3 (pp.88-89): (68-78)x2,92,100,(121-126)

§2.4 (pp.99-101): (2-14)x2,(26-32)x2,(40-68)x4,(78-84)x2, 90,92,100
102, (107-110)

§2.5 (108-109): 2,4,(5-8),10,12,(20-32)x2,38,40,44,48,50,64,(71-74)

Week 3

Monday = Labor Day

No class

Limits Review

Definition of Derivative

§3.1 (p.123): 6,8,10,12,16,18,22,24
(Use Limit Definition of Derivative only)

Review for Test 1 (p.111-112): 4,6,7,8,(12-26)x2,30,32,34,36,40,42,
48,52,54,55,56,58,64,65,72,75,83
(p.196): 2,3

Week 4

Test 1: Limits;
Definition of Derivative; Precalculus Review

Definition of Derivative

Derivatives and Continuity

Constant Rule

Power Rule

Constant Multiple Rule

Sum and Difference Rules

§3.1 (pp.123-124): 34,36,(39-42),50,53,54,66,74,76,78,80, (93-96)

§3.2 (pp.135-136): (4-64)x2, 68,80, (87-92)

Week 5

Derivatives: Sine and Cosine

Derivatives: Exponential, e^x

Product Rule

Quotient Rule

Derivatives: Trig Functions

Higher Order Derivatives

Chain Rule

Simplifying after Chain Rule

§3.3 (pp.146-149): (2-12)x2, (22-32)x2, 40, (42-58)x2,(68-74)x2,
80,82,88,92,96,(98-114)x2,(116-118),134,
136,(137-142)

§3.4 (pp.160-163): (8-32)x4,(48-120)x4,(126-132)x2, (140-152)x4,
(159-162), 164,172,174,181,(182-186)x2

§3.5 (pp.171-172): 2,6,10,14,18,22,(26-32)x2,38,40,46,48,(54-58)x2,
(68-76)x2

Week 6

Implicit Differentiation

Derivatives: Natural Log

Derivatives: Exponential, a^x

Derivatives: Log (general)

Logarithmic Differentiation

Derivatives of Inverses

Related Rates

§3.6 (pp.178-179): 2,6,10,16,(24-36)x4,50,62

§3.7 (pp.186-189): 14,16,18,20,24,26,29,30,38,42,43,48

Review for Test 2 (pp.196-198): (8-88)x4, (94-104)x2, 116,118

Week 7

Derivatives Review

Test 2: Derivatives

Curve Sketching: Overview

Week 8

First and Second Derivatives and the graph of a function

Rolle’s Theorem

Mean Value Thm: Derivative

First Derivative Test

Extrema of a Function

Relative Extrema

Critical Numbers

Concavity

Second Derivative Test

Curve sketching:
--Polynomial Functions

§4.1 (pp.207-209): (2-20)x2, (24-44)x4, (63-68),70,(73-76),78

§4.2 (pp.214-216): 6, (12-24)x4,32,34,38,(40-52)x4,66,(81-84)

§4.3 (pp.223-226): (4-20)x2, (24-64)x4,(75-80),(82-88)x2,102,104
(111-116)

Week 9

Curve Sketching:

--Rational Functions

Limits at Infinity

Curve sketching:

--Trigonometric Functions

Curve Sketching:

--Exponential/Logarithmic Functions

Curve Sketching Strategy

§4.4 (pp.232-234): (4-56)x4, (69-72), 78, (91-94)

§4.5 (pp.242-245): (1-6), (16-40)x4,(64-78)x4, (109-110)

§4.6 (pp.253-254): (4-32)x4, (42-50)x2,(65-68)

Week 10

Optimization Problems

Differentials

Review for Test 3

§4.7 (pp.262-265): 4,6,16,18,22,24,33,34,36,38,41

§4.8 (pp.272-273): (8-24)x2,30,32,34,40,42,44,(51-54)

Review for Test 3 (pp.274-276): (4-48)x4, 50,56,58,62,64,66,74,80,83
86,92

Week 11

Test 3: Curve Sketching;

Applications of Derivatives

Antiderivatives

Differential Equations

Basic Integration Rules

Algebra 1^st —Then Calculus

§5.1 (pp.287-289): (2-32)x2,36,40, 52, (53-57), 59,61,64,66

Week 12

Fund. Theorem of Calculus

Finding Area Under Curve

Integration by Substitution

Change of Variables

Log Rule Integration

Long Division

Integrals of Trig Functions

§5.4 (pp.324-327): (8-36)x4, (38-48)x2, 70

§5.5 (pp.337-340): (8-28)x4, (34-54)x2, (62-80)x2, (111-116)

§5.7 (pp.354-356): (4-40)x4, (52-58)x2,70,72, (105-108)

Week 13

Sigma Notation

Approximating Area

Area: Limit Definition

Riemann Sum

Definite Integrals

Definite Integral Properties

Average Value of Function

Mean Value Thm: Integrals

§5.2 (pp.299-301): 2,6,(8-24)x4,28,30,32,36,38,40,42,46,48,50,76,78

§5.3 (pp.309-312): (4-32)x4, (37-48),51,52,53, (63-72)

Week 14

2^nd Fund. Thm of Calculus

Net Change Theorem

Inverse Trig. Functions

Integration Practice

Review for Test 4

§5.4 (pp.324-327): (50-60)x2, 72,76,78,80,84,88,92,(93-98), 102,104
109,110

§5.8 (pp.362-363): (4-40)x4, (47-50)

Review for Test 4 (pp.375-376): (2-24)x2, 30, (32-68)x4, 42, 74,76,80

Week 15

Test 4: Integration

Final Exam Review

Week 16

Final Exam

Wednesday December 7^th

Last day to withdraw from a course with a “W” is November 3^rd.

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Syllabus File(s)

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Course Title: Calculus I
Course Prefix & Number: Math2413	Section Number: 400	Semester: 161S
Semester Credit Hours: 4	Lecture Hours: 64	Lab Hours:
Course Description (NCTC Catalog): Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas.
Course Prerequisite(s): MATH 2412 Pre-Calculus Math or equivalent preparation
Required or Recommended Course Materials: Calculus: Early Transcendental Functions, 6th Edition Ron Larson, Bruce H. Edwards Scientific calculator

Name of Instructor:	Benjamin Owens
Campus/Office Location:	Corinth Campus room 233
Telephone Number:	940-668-7731 x4501
E-mail Address:	bowens@nctc.edu

	At the successful completion of this course the student will be able to:
1	Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals
2	Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.
3	Determine whether a function is continuous and/or differentiable at a point using limits.
4	Use differentiation rules to differentiate algebraic and transcendental functions.
5	Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.
6	Evaluate definite integrals using the Fundamental Theorem of Calculus.
7	Articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.

# of Graded Course Elements	Graded Course Elements	Percentage or Point Values
24	In Class Quizzes	20
4	Tests	60
1	Final Exam	20