• General description from Clark's Academic Catalog
  Math 120, 121 and 122 (Calculus I, II, and III) / Lecture

  Calculus is essential for majors in biology, chemistry, computer science, mathematics, physics, and environmental science and policy. Part I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value theorem, and various applications. Part II includes; Riemann sums and integrals, techniques and applications of integration, improper integrals, transcendental functions; (logarithms, exponential functions, and inverse trigonometric functions). Part III includes further topics from calculus proper (sequences, series, polar coordinates) and introduces linear algebra (vectors, matrices, and linear systems). Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. Math 120, 121, and 122 each fulfill the Formal Analysis requirement. Prerequisite for Math 120: appropriate score on the mathematics placement test, or appropriate grade in Math 119. Prerequisite for Math 121: Math 120, or Math 124, or AP credit in Calculus. Prerequisite for Math 122: Math 121. / Offered every fall (120, 122) and spring (121).
  

• Course Hours. MWF 9:00–9:50.

• Office hours.

• Course Schedule

• Web pages for related courses
  Math 120, Calculus I
  Math 121, Calculus II
  Math 130, Linear Algebra
  Math 131, Multivariate Calculus

• Syllabus
  • Polar coordinates and parametric equations (chapter 10, about 8 meetings) including
    area in polar coordinates, curves given parametrically, tangents to parametric curves, areas under parametric curves, arclength, speed, area of a surface of revolution, cycloids
  • Infinite sequences and indeterminate forms (chapter 11, about 8 meetings) including
    the least upper bound axiom for real numbers, infinite sequences of real numbers, limits of sequences, convergence and divergence of sequences, pinching theorem, indeterminate forms, L'Hôpital's rule, improper integrals
  • Infinite series (chapter 12, about 11 meeetings) including
    Σ notation, infinite series (sums) of real numbers, convergence and divergence of series, geometric series, various tests for convergence (integral, comparison, limit comparison, root, ratio) conditional and absolute convergence, Taylor polynomials and Taylor series, Lagrange's remainder formula, power series, interval and radius of convergence, differentation and integration of power series, binomial series
  • Linear algebra in three dimensions (chapter 12 and appendix A2, about 10 meetings) including
    distance in three dimenions, vectors, algebra of vectors, norm (length) of a vector, triangle inequality, dot products (a.k.a inner products or scalar products), parallel and perpendicular vectors, direction angles and direction cosines, Cauchy-Schwarz inequality, cross products (a.k.a. outer products or vector products), scalar triple products, lines and planes, normal vectors to planes, and determinants
  
  
• Course administration. There will be quizzes, two midterms, and a final exam.

  Homework and Quizzes. I will assign daily practice exercises from the text to help you master the concepts discussed in class. Although the exercises will not be collected regularly, you are expected keep up to date on the problems. Math is not a spectator sport. You learn by doing; therefore, it is only to your advantage to keep abreast of the current topics under discussion. Periodically I will assign a few specific exercises to be collected and graded, and those assignments are due in class on the assigned day; I won't accept late assignments. I'll give short 15–20 minute quizzes periodically throughout the semester.

  Exams are in class, closed book, and closed notebook, but you may use one sheet of notes and a calculator. If you have a legitimate, documented excuse for missing an exam, contact me (before the scheduled time if at all possible) to reschedule the exam (at my convenience).

  The final exam will be a two-hour, comprehensive exam, given during the final exam period. All students will be required to take the final exam at that time. Therefore do not make plans to leave campus before the final exam.

  The course grade is computed as follows

     20%, Assignments and quizzes 
     25%, Exam 1     
     25%, Exam 2     
     30%, Final Exam 
  

• Work expectation. You will work on average about six to eight hours each week outside of class. This will include studying from your notes and the textbook, doing the homework assignments, and studying for quizzes and exams. See About studying mathematics in general, and Calculus in particular for more details.

• Textbook. Salas, Hillie, & Etgen. Calculus: One and Several Variables, 10th edition.

• Tutoring
  Sunday through Thursday evenings, 8-10 p.m., room BP 312.

• Practice exercises.

  Polar coordinates, parametric equations
  § 10.2   # 1–23 odd, 37, 41, 46, 49, 51, 54, 57, 59
  § 10.3   # 1–13 odd, 21, 23, 27, 29
  § 10.4   # 3, 5, 9, 15, 17, 19, 23, 27
  § 10.5   # 1, 3, 5, 9, 13, 22, 23, 33
  § 10.6   # 3, 5, 19, 36
  § 10.7   # 3, 5, 19–23 odd, 31, 35
  § 10.8   # 11–17 odd
  Project 10.8 # 1, 2
  
  Sequences, indeterminate forms, improper integrals, L'Hôpital's rule
  § 11.1   # 5–17 odd, 21, 23, 27
  § 11.2   # 5, 7, 9, 11, 13, 23, 31, 41, 49, 54
  § 11.3   # 5, 7, 9, 10, 13, 17, 21, 58
  § 11.4   # 1, 3, 11, 13, 17, 21, 25, 33, 41
  § 11.5   # 1, 5, 7, 9, 21, 23, 43
  § 11.6   # 1, 3, 7, 11, 15, 17, 25, 31, 35, 47, 49
  § 11.7   # 1, 3, 9, 13, 15, 19, 25, 27, 33
  
  Infinite series 
  § 12.1   # 1–9 odd, 17–29 odd
  § 12.2   # 1, 5, 7, 11, 13, 15, 17, 21, 29, 37
  § 12.3   # 1, 3, 5, 11, 13, 15, 25, 27, 29, 35
  § 12.4   # 1, 3, 5, 9, 11, 17, 21, 25, 33
  § 12.5   # 1, 3, 7, 10, 11, 16, 27, 28, 30, 31
  § 12.6   # 1, 5, 7, 14, 15, 21, 23, 27, 33, 41
  § 12.7   # 3, 5, 9, 11
  § 12.8   # 3, 5, 9, 13, 15, 35, 37
  § 12.9   # 1, 5, 11, 15, 21, 27, 41
  Project 12.9A # 1, 2, 3, 4, 5a, 6
  
  Vectors in three dimensions
  § 13.1   # 3, 7, 15, 19, 23, 25, 31, 33
  § 13.2   # 1–13 odd, 25, 29, 40
  § 13.3   # 3, 5, 7, 11, 17
  § 13.4   # 3–11 odd, 21–27 odd
  § 13.5   # 1, 3, 5, 13, 21
  § 13.6   # 1, 3, 5, 11, 17, 19
  Appendix A.2   # 1–7 odd, 11, 13
  

• Notes and Tests
  • Sample first test
  • First test, answers
  • Notes on power series
  • Sample second test
  • Second test, answers

• Interesting Web Sites
  • Humor in mathematics
  • Dave's Short Trig Course, and Dave's Short Course on Complex Numbers.
  • The Little Gallery of Roulettes
  • Math Archives links for
    • Calculus resources on line
    • Linear and Matrix Algebra
    • Visual calculus
  • The MacTutor History of Mathematics archive including articles by J J O'Connor and E F Robertson on
    • The history of calculus
    • The history of abstract linear spaces
    • The history of matrices and determinants
  • Dave Rusin's The Mathematical Atlas describes the subject of linear algebra and its subfields, at Northern Illinois University.
  • On-line textbooks on linear algebra:
    • Linear Algebra: An Introduction to Linear Algebra for Pre-Calculus Students. by Tamara Anthony Carter, Richard A. Tapia, and Anne Papakonstantinou, at Rice University.
    • Linear Algebra by Jim Hefferon, at Saint Michael's College.
    • Elementary Linear Algebra, lecture notes by Keith Matthews.
    • Linear Algebra and Applications Textbook by Thomas S. Shores.
  
  

This page is located at http://aleph0.clarku.edu/~djoyce/MA122/