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# Math 8 Calculus 2 Syllabus **Instructor:** Bon-Soon Lin  **Textbook:** Calculus (Stewart, Clegg, Watson, 9E) **Lecture times and location:** 06:30PM-09:15PM MTWH at MC 66 **Class dates:** Tuesday June 20, 2023 to Thursday August 10, 2023 **Office hours:** Zoom, maybe Friday evening at 630PM~730PM+, or Saturday morning? **Math lab tutoring:** There is free tutoring available to you M-F 8 am-10 pm and Saturday 10 am - 630 pm. See website [https://www.smc.edu/student-support/academic-support/tutoring-centers/math-lab/](https://www.smc.edu/student-support/academic-support/tutoring-centers/math-lab/) ## Course information. You are expected to be an independent and responsible learner, so we can use our time together effectively. Since this is a summer course, the course would be quite fast paced. You are expected to have read the assigned section in the textbook for that day before we meet. I invite you to ask questions and engage with people during our meetings. And I hope our meetings are something you look forward to each week! We will follow the textbook rather closely, as it is your other resource. I recommend you find a copy of the textbook. If you can find an older edition that is fine as well (the material should roughly be the same).   ## Course description. This second course in calculus is intended primarily for science, technology, engineering, and mathematics majors. Topics 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. ## Main Course topics.  1. Inverse functions, transcendental functions, and L’Hospital’s rule.   2. Integration techniques, approximations and improper integrals.   3. Sequences and series, tests for convergence.  4. Power series and Taylor series representations of a function. 5. Further applications of calculus, parametric and polar calculus, conic sections.  ## Course pre-requisite: Math 7. You should be familiar with materials from Math 7 or equivalent Calculus 1 courses. Topics should be familiar to you: **Limits** (precise definition and intuitive meaning, limit laws), **continuity** (precise definition, continuity laws, extreme value theorem, intermediate value theorem), **differentiability** (precise definition, derivative rules, product and quotient rule, chain rule, Rolle’s theorem, mean value theorem), **integration** (Riemann sum definition, geometric meaning, indefinite integrals, fundamental theorem of calculus I and II, u-substitution), and **applications of differentiation** (tangent lines, rate of change, implicit differentiation, related rates, optimization, curve sketching), as well as **applications of integration** (arclength, volumes and areas, volumes by cross section, volumes of revolutions by cross section and shell method). ## Student Learning Objectives. 1. Set up and solve applications problems involving limits, areas, volumes, arc length, indeterminate forms, center of mass and improper integrals using differentiation and integration techniques with transcendental functions.  2. Determine the divergence or type of convergence of various infinite series, find the domain (interval of convergence) of power series and derive and apply Taylor series.  3. Graph and analyze curves using parametric equations and/or polar coordinates and solve applications involving functions in either polar or parametric form. ## Grading. 10% Homework (completion based, to be checked by each exam) 20% Exam 1 **July 6 Week 3 Thursday** 20% Exam 2 **July 31 Week 7 Monday** 50% Final Exam **August 10 Week 8 Thursday**