MATH 8 CALCULUS II Course Syllabus Spring Session, 2014 Instructor: Brian Rodas Class Room and Time: MC82 M-Th 12:45pm-1:50pm Office Room: MC35 Office Phone: (310)434-8673 Office Hours: M 11-12pm, TTh 2:30pm-3:30pm, W 2:30pm-3:30pm(Math Study Room MC 84) and by appointment E-mail: rodas brian@smc.edu Class Website: http://homepage.smc.edu/rodas brian Text: Swokowski, Earl. Calculus. Classic edition, Brooks/Cole Publishing Co.,1991. Course Description: This course is intended for computer science, engineering, mathematics and natural science majors. Topics in this second course include derivatives and integrals of transcendental functions with mathematical and physical applications, indeterminate forms and improper integrals, infinite sequences and series, and curves, including conic sections, described by parametric equations and polar coordinates. The prerequisite is MATH 7 with a grade of C or better. Format of Course: The first 10 minutes of each class will be devoted to addressing students questions regarding homework or material from the previous section. The remainder of the class will be spent presenting new material. Homework: Homework will be assigned daily but not collected. The problems assigned are practice problems in understanding the material covered for the day. It has been known that a genuine understanding and completion of the homework results in quality performance. Worksheets: Worksheets will be given periodically. They consist of problems designed to understand the material and promote cooperative learning. These problems are to be done in groups. They will be collected and graded. Quizzes: Quizzes will be given periodically. They will be approximately 10-15 minutes long. It has been my nature to give quiz problems identical to the homework. Therefore it would be in your best interest to do the homework. Each quiz is worth ten points. The two lowest quiz scores will be dropped. Exams: There will be four exams and a final. Each exam is worth 100 points. The lowest exam will be scaled out of 50 points. So if your test scores are 100, 90, 80, and 70, then your test average is (100+90+80+35)/350. The final is worth 200 points and is cumulative. You must show all necessary work to receive full credit. Note also that a diagnostic mini-exam will be given on the fourth class. This is a mandatory exam that every student must take to stay in the class. It will be graded and factored into the quiz grade. Calculators: Although the use of calculators are not permitted for exams or quizzes, they can be useful for doing tedious calculations and graphing. I encourage you to check your answers on the calculator when doing your homework but do not become dependent on the calculator. They will be extremely handy for graphing parametric and polar curves. Grading: Top three exams Lowest exam Quizzes Worksheets Final exam Total 300 points 50 points 70 points 30 points 200 points 650 points
The expectation is that a letter grade will be given using the following scale for the semester average: 90-100%(A), 80-89%(B), 70-79%(C), 60-69%(D), 0-59%(F). Academic Conduct: You are expected to abide by Santa Monica College s code of academic conduct on all exams, quizzes and homework. Copying homework solutions or quiz or test answers from someone is considered cheating as is altering a quiz or examination after it has been graded or giving answers to someone during an exam or quiz. If caught cheating, the parties involved will receive a zero on the exam and an academic dishonesty report will be filed. Also note that cell phones are to be turned off for the duration of each class. Since attendance is essential for normal progress in class, a student is expected to be in class regularly and on time. Missing classes puts you in danger of being dropped. There are no makeup assignments, quizzes or exams. Late assignments will not be accepted. No excuses. Refer to the school s web page, www.smc.edu, for withdrawal dates. IT IS THE STUDENT S RESPONSIBILITY TO BE AWARE OF WITHDRAWAL DATES AND TO TAKE THE AP- PROPRIATE NECESSARY STEPS. If a student does not withdraw and stops coming to class, the student will receive a failing grade. Entry Skills for Math 8: Prior to enrolling in Math 8 students should be able to: A. Evaluate limits using basic limit theorems and the epsilon-delta definition. B. State and apply the definition of continuity to determine a function s points of continuity and discontinuity. C. Differentiate elementary functions using basic derivative theorems and the definition of the derivative. D. Integrate elementary functions using basic derivative theorems and the definition of the definite integral. E. Approximate definite integrals using numerical integrations. F. Solve derivative application problems including optimization, related rates, linearization, curve sketching, and rectilinear motion. G. State integral application problems including area, volume, arc length and work. H. State and apply the Mean Value Theorem, Extreme Value Theorem, Intermediate Value Theorem, Fundamental Theorem of Calculus and Newton s Method. Exit skills for MATH 8: Upon successful completion of this course, the student will be able to: A. Differentiate and integrate hyperbolic, logarithmic, exponential and inverse trig functions. B. Evaluate integrals using techniques including integration by parts, partial fractions, trig integrals and trig and other substitutions. C. Solve integral application problems including suface area of revolutions and center of mass. D. Identify and evaluate indeterminate forms and improper integrals using techniques including L Hopital s Rule. E. Graph polar curves and curves described by parametric equations. F. Determine whether an infinite series converges absolutely, converges conditionally or diverges using techniques including direct comparison, limit comparison, root, ratio, integral, p-series, nthterm and alternating series tests. G. Determine the radius and interval of convergence of a power series. H. Compute the sum of a convergent geometric series and a convergent telescoping series. I. Determine the Taylor Series of a given function at a given point.
SCHEDULE OF LECTURES, HOMEWORK & EXAMS Date Section Material Homework 2/18 Calculus Review Review sections 2.6 2/19 Calculus Review 3.9,4.9 Do all odd problems. 2/20 Calculus Review Section 5.8odd, 6.9:1-13odd 2/24 Calculus 1 Review/Exam 2/25 7.1 Inverse Functions 1-17odd,21-31odd 2/26 7.2 The Natural Logarithm 1-47odd,53 2/27 7.3 The Exponential Function 1-45odd 3/3 7.4 Integrals 1-45odd 3/4 7.5 Logarithms & Exponentials with base b 1-45odd 7.6 Growth and Decay(self-study) 1-19odd 3/5 8.1 Inverse Trig Functions 1-29odd 3/6 8.2 Derivatives & Integrals of Inverse Trig Fcns. 1-43odd,51 3/10 10.1 Indeterminate forms 1-49odd 3/11 10.2 Other indeterminate forms 1-41odd 3/12 8.3 Hyperbolic Functions 3-41odd 3/13 Worksheet for Exam 1 3/17 REVIEW 3/18 No class 3/19 EXAM 1 on Ch.7, 8, Sections 10.1 & 10.2 3/20 9.1 Integration by Parts 1-37odd 3/24 9.2 Trig Integrals 1-31odd 3/25 9.3 Trig Substitution 1-23odd 3/26 9.4 Rational functions 1-19odd 3/27 9.5 Quadratic Expressions 1-19odd 3/31 9.6 Misc. Substitutions 1-19odd,27,29 4/1 10.3 Integrals with Infinite Limits 1-23odd,35 4/2 10.4 Discontinuous Integrands 1-23odd,35 4/3 Worksheet for Exam 2 4/7 REVIEW 4/8 EXAM 2 on Ch.9, Sections 10.3 & 10.4 4/9 11.1 Sequences 1-41odd 4/10 11.1 Sequences 1-41odd SPRING BREAK 4/14-4/18 4/21 11.2 Infinite Series 1-3,7-15odd,21,25,29, 33-47odd,55 4/22 11.3 Positive Term Series 1-47odd 4/23 11.3 Positive Term Series 1-47 odd 4/24 11.4 Ratio and Root Tests 1-37odd 4/28 11.5 Alternating Series 1-31odd Absolute Convergence 4/29 11.6 Power Series 1-29odd,33 4/30 11.7 Power Series Representations 1-9odd,15-27odd 5/1 11.8 MacLaurin & Taylor Series 1-29odd 5/5 11.9 Applications of Series 1,7,9,15,17,21,27 5/6 11.10 Binomial Series 1-13odd 5/7 Worksheet for Exam 3 5/8 REVIEW
5/12 EXAM 3 on Ch. 11 5/13 13.1 Plane Curves 1-29odd 5/14 6.5 Surface Area 29-39odd 5/15 13.2 Tangent Lines and Arc Length 1-17odd,21-25odd,29,31 5/19 13.2 Tangent Lines and Arc Length 1-17odd,21-25odd,29,31 5/20 13.3 Polar Coordinates 1-49odd 5/21 13.3 Polar Coordinates 1-49odd 5/22 13.4 Integrals in Polar Coordinates 1-31odd 5/26 Holiday (No class) 5/27 13.4 Integrals in Polar Coordinates 1-31odd 5/28 13.5 Polar Equations of Conic Sections 1-9odd 5/29 6.7 Moments and Center of Gravity 1-14odd 6/2 Worksheet for Exam 4 6/3 REVIEW 6/4 EXAM 4 on Ch. 13, Sections 6.5 & 6.7 6/5 REVIEW for final 6/9 REVIEW for final 6/10 FINAL EXAM 12pm-3pm The instructor does reserve the right to add or modify the syllabus.
Course Content: 8% -Review topics from precalculus (algebra functions, trigonometry, sequences, series) 13% -Limits and continuity (epsilon-delta, limits, one-sided limits, limits involving infinity, definition & properties of continuous functions) 21% -Derivatives (definition, techniques of differentiation, derivatives of rational & trig functions, Chain Rule, differentials & linearization, implicit differentiation, tangent lines, rates of change) 23% -Applications of the derivative (extreme values of functions, the Mean Value Theorem, the first and second derivative tests, curve sketching, optimization, rectilinear motion, Newtons Method) 17% -Integrals (antiderivatives, indefinite integrals, definite integral, Fundamental Theorem of Calculus, Mean Value Theorem for integrals, numerical integration) 14% -Applications of the definite integral (area; volumes by slicing, disks, washers, cylindrical shells; arc length; work) 4% -Review for final exam Student Learning Outcomes: The knowledge, skills, or abilities that the student will demonstrate by the end of the semester. Given an algebraic or trigonometric function, students will evaluate and apply limits and prove basic limit statements. Given an algebraic or trigonometric function, students will differentiate the function and solve application problems involving differentiation. Given an algebraic or trigonometric function, students will integrate the function and solve application problems involving integration.