Calculus 1 and 2

Have I not commanded you?

Be strong and courageous.

Do not be afraid; do not be discouraged,

for the Lord you God will be with you wherever you go.

Joshua 1:9 (NIV)

MTH 281

Calculus I

Syllabus

Instructor: Larry Latona

MTH 281 – Calculus I

4 Credits

Prerequisites: High school algebra or trigonometry

COURSE DESCRIPTION: This course is an introduction to the elements of differential and integral calculus.

COURSE OBJECTIVES

Specifically:

· understand the basics of trigonometry and trigonometric identities

· understand what a function is and specify its characteristics

· be able to define a function and determine the domain and range of a function

· understand the concept of a limit

· be able to evaluate the limits of continuous and non-continuous functions

· understand the concept of a derivative

· be able to determine derivatives of several types of functions

· be able to differentiate implicitly

· be able to know when to solve problems by using differentiation

· understand the concept of an integral

· be able to determine integrals of several types of functions

· be able to know when to solve problems by using integration

Generally:

TEXT AND COURSE MATERIALS/RESOURCES

Calculus by Finney,Demana,Waits, Kennedy

Calculus (5th Ed) by Larson, Hostetler, and Edwards

COURSE OUTLINE/CALENDAR (with topics, readings, assignments, due dates)

CHAPTER 1 Prerequisites for Calculus page 2

1.1 Lines 3

1.2 Functions and Graphs 12

1.2 Functions and Graphs 12

1.3 Exponential Functions 22

1.4 Parametric Equations 30

1.5 Functions and Logarithms 37

CHAPTER 2 Limits and Continuity 58

2.1 Rates of Change and Limits 59

2.2 Limits Involving Infinity 70

2.3 Continuity 78

CHAPTER 3 Derivatives 98

3.1 Derivative of a Function 99

3.2 Differentiability 109

3.3 Rules for Differentiation 116

3.4 Velocity and Other Rates of Change 127

3.5 Derivatives of Trigonometric Functions 141

3.6 Chain Rule 148

3.7 Implicit Differentiation 157

3.8 Derivatives of Inverse Trigonometric Functions 165

3.9 Derivatives of Exponential and Logarithmic Functions 172

Test Chap 3

CHAPTER 4 Applications of Derivatives 186

4.1 Extreme Values of Functions 187

4.2 Mean Value Theorem 196

4.3 Connecting ƒD and ƒD with the Graph of ƒ 205

4.4 Modeling and Optimization 219

4.5 Linearization and Newton’s Method 233

CHAPTER 5 The Definite Integral 262

5.1 Estimating with Finite Sums 263

5.2 Definite Integrals 274

5.3 Definite Integrals and Antiderivatives 285

5.4 Fundamental Theorem of Calculus 294

CHAPTER 6 Differential Equations and

6.1 Slope Fields and Euler’s Method 321

6.2 Antidifferentiation by Substitution 331

6.3 Antidifferentiation by Parts 341

6.4 Exponential Growth and Decay 350

6.5 Logistic Growth 362 Test Chap 6

CHAPTER 7 Applications of Definite Integrals 378

7.1 Integral As Net Change 379

7.2 Areas in the Plane 390

7.3 Volumes 399

7.4 Lengths of Curves 412

7.5 Applications from Science and Statistics 419 Test chap 7

Review for Final Final exam

GRADING SYSTEM

COURSE POLICIES

OUR LEARNING COMMUNITY/RESPECT FOR DIVERSITY STATEMENT

As a Christian college, Roberts Wesleyan College seeks to create an inclusive learning community that recognizes and values human diversity as a reflection of the Kingdom of God, esteems all people, and prepares students to serve in a global environment. Faculty and students alike are expected to contribute to a classroom environment in which all individuals feel safe, welcomed, valued, and respected, and diverse perspectives can be shared, heard, and examined critically.

ACADEMIC INTEGRITY STATEMENT

Roberts Wesleyan College seeks to promote personal and intellectual integrity within the academic community. Honesty and trustworthiness are notonly fundamental principles of the Judeo-Christian tradition, but essential practices within academe. The following behaviors are, therefore,unacceptable:

· Cheating in its various forms: e.g.,

o Copying another student’s work

o Allowing work to be copied

o Using unauthorized aids on an examination

o Obtaining any part of an examination prior to its administration

o Fabricating research data

o Submitting another person’s work as one’s own

o Receiving credit falsely for attendance at a required class or activity

· Plagiarizing (i.e. presenting someone else’s words or specific ideas as one’s own, including inadequate documentation of sources and excessivedependence on the language of sources even when documented). All quoted material and ideas taken from published material, electronic media, andformat interviews must be cited: direct quotations must be enclosed in quotation marks. Therefore, whether quoting or paraphrasing, include anappropriate reference to the source (in-text citation) and a Reference page. Refer to the APA Manual for proper citation formats; consult theinstructor regarding preferred citation style. (American Psychological Association—APA.).

· Violating copyright laws and license agreements, including but not limited to:

o Making illegal single copies of music or other print materials

o Making and/or distributing unauthorized copies of computer software

and/or digital information

· Denying others appropriate access to information in the classroom, library or laboratory including but not limited to:

o Removing pages from books or journals

o Hiding or intentionally damaging materials or electronic information

· Destroying, altering, or tampering with someone else’s work.

· Submitting the same or similar work for more than one course or assignment without prior approval from the professors.

· Destroying, altering or tampering with academic or institutionalrecords.

Students who violate the Academic Integrity Policy shall be subject to disciplinary action as outlined in the Student Handbook and FacultyHandbook.

CLASS ATTENDANCE

Students are expected to attend all sessions of the courses for which they are registered.

All excuses for class absence should be presented to the instructor in advance when possible. Make-up of work missed can then be arranged. Absences for college-sponsored activities, including athletic participation and field trips, both on and off-campus, are regarded as excused, and all work may be made up without penalty. Unavoidable absence due to documented illness, death of a close relative, or other emergency beyond the control of the student is excusable and the work missed may be made up.

It is the responsibility of the student to contact her or his instructor(s) regarding the reason for an absence. All excuses for class absence should be presented to the instructor in advance when possible. Make-up of work missed can then be arranged. When an instructor finds that a student is failing because of excessive absence, whether excused or unexcused, the instructor may recommend that the student be dropped from the course.

MTH 282 Calculus II Syllabus Fall 2020 Allrightsreserved on the Syllabus/Student Guide July 29, 2020 MTH 282 – Calculus II / Fall 2020 ROBERTS WESLEYAN COLLEGE Instructor: Larry Latona MTH 282 – Calculus II 4 Credits Prerequisites: MTH 281 -Calculus I COURSE DESCRIPTION: This course is a continuation of MTH 281 with an emphasis on transcendental functions, techniques of integration, applications of integration, and infinite series. More meaningful description: Calculus reaches out to a wide range of fields that use its principles to construct mathematical models that bring understanding of the world around us. Some of the fields of study that use calculus are economics, biology, medical research, space exploration, psychology, physics, engineering, physiology, education, computer science, and actuarial science. The material presented in this course is intended to provide students with the mathematical skills necessary to be successful not only in subsequent calculus courses and advanced math courses, but also in related areas. As a continuation of Calculus I, this course includes applications of the definite integral, inverse functions, techniques of integration, parametric equations, and infinite sequences and series. Informally, this course provides insight into the question “How do I integrate that?” opportunities to practice techniques of integration in a variety of mathematical and physical applications, and (through study of numerical integration, sequences and series) some approaches to approximation. COURSE OBJECTIVES 1. Thorough understanding of and ability to apply the fundamental concepts, definitions, theorems, and techniques of calculus. 2. Ability to communicate mathematical ideas to peers. 3. Use of appropriate technology (e.g., graphing calculators, computer algebra systems, spreadsheets) 4. Use of calculus in modeling various physical, biological and social phenomena. 5. Growing awareness of the breadth of mathematical activity. A more detailed list of competencies is available from the instructor. TEXT AND COURSE MATERIALS/RESOURCES Calculus by Ron Larson; Bruce H. Edwards 9781337286886 11th Edition | Previous Editions: 2014, 2010, 2006, ©2018, Published MTH 282 – Calculus II / Fall 2020 ROBERTS WESLEYAN COLLEGE COURSE OUTLINE/CALENDAR (with topics, readings, assignments, due dates) Classroom discussion and lectures may not always coincide exactly with the outline but will deal with the same basic material in roughly the same time frame 7.1 Area of a Region Between Two Curves Area of a Region Between Two Curves Area of a Region Between 7.2 Volume: The Disk Method The Disk Method The Washer Method Solids with Known Cross Sections 7.3 Volume: The Shell Method The Shell Method Comparison of Disk and Shell 7.4 Arc Length and Surfaces of Revolution Arc Length Area of a Surface of Revolution 7.5 Work Work Done by a Constant Force Work Done by a Variable Force. 8.1 Basic Integration Rules Fitting Integrands to Basic Integration Rules 8.2 Integration by Parts Integration by Parts 8.3 Trigonometric Integrals Integrals Involving Powers of Sine and Cosine Integrals Involving Powers of Secant and Tangent Integrals Involving Sine-Cosine Products 8.4 Trigonometric Substitution Trigonometric Substitution Applications 8.5 Partial Fractions Partial Fractions Linear Factors Quadratic Factors 8.6 Numerical Integration The Trapezoidal Rule Error Analysis 8.8 Improper Integrals Improper Integrals with Infinite Limits of Integration Improper Integrals with Infinite Discontinuities 9.1 Sequences Limit of a Sequence Pattern Recognition for Sequences Monotonic Sequences and Bounded Sequences 9.2 Series and Convergence Infinite Series Geometric Series nth-Term Test for Divergence 9.3 The Integral Test and -Series The Integral Test -Series and Harmonic Series 9.4 Comparisons of Series Direct Comparison Test Limit Comparison Test 9.5 Alternating Series Alternating Series Alternating Series Remainder Absolute and Conditional Convergence Rearrangement of Series 9.6 The Ratio and Root Tests The Ratio Test The Root Test Strategies for Testing Series 9.7 Taylor Polynomials and Approximations Polynomial Approximations of Elementary Functions Taylor and Maclaurin Polynomials Remainder of a Taylor Polynomial 9.8 Power Series Power Series Radius and Interval of Convergence Endpoint Convergence Differentiation and Integration of Power Series 9.9 Representation of Functions by Power Series Geometric Power Series Operations with Power Series 9.10 Taylor and Maclaurin Series Taylor Series and Maclaurin Series Binomial Series Deriving Taylor Series from a Equations Eliminating the Parameter Finding Parametric Equations 10.3 Parametric Equations and Calculus Slope and Tangent Lines Arc Length Area of a Surface of Revolution 10.4 Polar Coordinates and Polar Graphs Polar Coordinates Coordinate Conversion Polar Graphs Slope and Tangent Lines Special Polar Graphs 10.5 Area and Arc Length in Polar Coordinates Area of a Polar Region Points of Intersection of Polar Graphs Arc Length in Polar Form Area of a Surface of Revolution MTH 282 – Calculus II / Fall 2020 ROBERTS WESLEYAN COLLEGE GRADINGSYSTEM The following table lists the percentages associated with each assessment. Quarter Grade : Homework 15% Quizzes 30% Test 55% Final Grade: Quarters 1 and 2, 80% Cumulative Final Exam 20% Course Final Grade Distribution A 93 and above C 73-76 A- 90-92 C- 70-72 B+ 87-89 D+ 67-69 B 83-86 D 63-66 B- 80-82 D- 60-62 C+ 77-79 F Below 60% COURSE POLICIES OUR LEARNING COMMUNITY/RESPECT FOR DIVERSITY STATEMENT As a Christian college, Roberts Wesleyan College seeks to create an inclusive learning community that recognizes and values human diversity as a reflection of the Kingdom of God, esteems all people, and prepares students to serve in a global environment. Faculty and students alike are expected to contribute to a classroom environment in which all individuals feel safe, welcomed, valued, and respected, and diverse perspectives can be shared, heard, and examined critically. ACADEMICINTEGRITYSTATEMENT Roberts Wesleyan College seeksto promote personal and intellectual integritywithin the academic community. Honesty and trustworthiness are not only fundamental principles of the Judeo-Christian tradition, but essential practices within academe. The following behaviors are,therefore, unacceptable: • Cheating in its variousforms: e.g., o Copying anotherstudent’s work o Allowing work to be copied o Using unauthorized aids on an examination o Obtaining any part of an examination priorto its administration o Fabricating research data o Submitting another person’s work as one’s own o Receiving creditfalsely for attendance at a required class or activity MTH 282 – Calculus II / Fall 2020 ROBERTS WESLEYAN COLLEGE • Plagiarizing (i.e. presenting someone else’s words or specific ideas as one’s own, including inadequate documentation ofsources and excessive dependence on the language of sources even when documented). All quoted material and ideastaken frompublished material, electronic media, and formatinterviews must be cited: direct quotations must be enclosed in quotation marks. Therefore, whether quoting or paraphrasing, include an appropriate reference to the source (in-text citation) and a Reference page. Refer to the APA Manual for proper citation formats; consult the instructorregarding preferredcitation style. (AmericanPsychological Association—APA.). • Violating copyrightlaws and license agreements, including but not limited to: o Making illegalsingle copies of music or other print materials o Making and/or distributing multiple copies of printed, copyrighted materialswithoutwrittenpermission o Making and/or distributing unauthorized copies of computersoftware and/or digital information • Denying others appropriate accessto information in the classroom, library or laboratory including but notlimited to: o Removing pagesfrom books orjournals o Hiding orintentionallydamaging materials or electronic information • Destroying, altering, ortampering with someone else’s work. • Submitting the same or similar work for more than one course or assignment without prior approval from the professors. • Destroying, altering or tampering with academic orinstitutionalrecords. Students who violate the Academic Integrity Policy shall be subject to disciplinary action as outlined in the Student Handbook and Faculty Handbook. CLASS ATTENDANCE Students are expected to attend all sessions of the courses for which they are registered. All excuses for class absence should be presented to the instructor in advance when possible. Makeup of work missed can then be arranged. Absences for college-sponsored activities, including athletic participation and field trips, both on and off-campus, are regarded as excused, and all work may be made up without penalty. Unavoidable absence due to documented illness, death of a close relative, or other emergency beyond the control of the student is excusable and the work missed may be made up. It is the responsibility of the student to contact her or his instructor(s) regarding the reason for an absence. All excuses for class absence should be presented to the instructor in advance when possible. Make-up of work missed can then be arranged. When an instructor finds that a student is failing because of excessive absence, whether excused or unexcused, the instructor may recommend that the student be dropped from the course.

Watch videos for chap 3

http://www.calculus-help.com/tutorials/

http://archive.org/details/ap_calculus_ab

Beginning Calculus site : http://www.calculus-help.com/funstuff/phobe.html

Calculus Notes: http://tutorial.math.lamar.edu/

POWER POINT NOTES BELOW