Syllabus

Regular and punctual attendance is expected of all students in all classes for which they have registered. Students are responsible for keeping up with what occurs in class when they are absent. Dropping a course is the student's responsibility, but you MAY be dropped for excessive absence. See Attendance Regulations in the North Central Texas College Catalog.

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.

DISABILITY SERVICES (OSD)

The Office for Students with Disabilities (OSD) provides accommodations for students who have a documented disability. On the Corinth Campus, go to room 170 or call 940-498-6207. On the Gainesville Campus, go to room 110 or call 940-668-4209. Students on the Bowie, Graham, Flower Mound, and online campuses should call 940-668-4209.

North Central Texas College is on record as being committed to both the spirit and letter of federal equal opportunity legislation, including the Americans with Disabilities Act (ADA) of 1990, ADA Amendments Act of 2009, and Section 504 of the Rehabilitation Act of 1973 (P.L. 93-112). http://www.nctc.edu/StudentServices/SupportServices/Disabilityservices.aspx

CORE CURRICULUM FOUNDATIONAL COMPONENT AREA______________________________

o Communication

x Mathematics

o Life and Physical Science

o Language, Philosophy & Culture

o Creative Arts

o American History

o Government/Political Science

o Social and Behavioral Sciences

o Component Area Option

REQUIRED CORE OBJECTIVES

x Critical Thinking

x Communication

x Empirical and Quantitative

o Teamwork

o Personal Responsibility

o Social Responsibility

COURSE TYPE

o Academic General Education Course (from ACGM but not in NCTC Core)

o Academic NCTC Core Curriculum Course

o WECM Course

STUDENT HANDBOOK

Students are expected to follow all rules and regulations found in the student handbook. http://nctc.smartcatalogiq.com/en/2014-2015/Catalog/North-Central-Texas-College-Student-Handbook

Name of Chair/Coordinator:	Keith Bailey
Office Location:	Cor335
Telephone Number:	940-498-6413
E-mail Address:	kbailey@nctc.edu
Name of Instructional Dean:	Sara Alford
Office Location:	Flower Mound 200C
Telephone Number:	972-899-8414
E-mail Address:	salford@nctc.edu

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

MATH 2413 400 - CALCULUS I

Introduction

Syllabus File(s)