MATH 115 - Preparation for Calculus - Spring 2012
Where: 23 PSYCH BLD
When: MWF 12:00-12:50
Final exam: 8:00-11:00 AM, Wednesday, May 9
Office hours: 4:00-5:00 PM Tuesday (or by appointment) in 222A Illini Hall
Tutoring: 4:00-6:00 PM Thursday in 241 Altgeld Hall and 4:00-5:00 PM Monday in 147 Altgeld Hall
Syllabus (exam dates are subject to change)
Announcements
- Final exam scores are posted in the usual place and final grades have been posted to self-service!
- Tutoring information from the Engineering department.
- You can check your homework and exam grades here (requires login with NetID).
- New extra tutoring will be held Mondays from 4 till 5 p.m. in 147 Altgeld Hall.
- I am also available in my office on Monday afternoons, but please schedule in advance!
- Department syllabus for 115 that I am following roughly.
- If you want additional textbook help I suggest "Precalculus: Mathematics for Calculus" by Stewart, Redlin and Watson (SRW). I will post readings from the 5th edition (there is a 6th edition available).
- Note that the two recommended books only supplement the lectures. Your lecture notes will be more valuable than any book!
- Click here for a math dep't link with more (including paid) tutoring options.
Homeworks
- Homework 8: Trig graphs: 15, 19, 21, 23, 25 (from 5.3) and 1-6, 15, 27, 43, 47 (from 5.4) (due Fri, 4/20) (solutions)
- Homework 7: Trig (angles): 1, 3, 15, 17, 21, 25, 27 and
Trig (radians): 19, 20, 29, 31 (from 5.1) and 3, 7, 11, 27, 35 (from 5.2) (due Fri, 4/13) (solutions: angles, radians)
- Homework 6: Inverse functions: 1, 3, 9, 11, 23, 29, 41, 45, 54 and Logarithmic functions: 25, 27, 31, 47 (from 4.2) and 1, 7, 11, 31 (from 4.3) (due Fri, 4/6) [this assignment is longer than average, but composed of easier problems!]
(solutions)
- Homework 5: Polynomial functions: 3, 5-10, 15, 21, 73 and Rational functions: 33, 37, 41, 75 (due Fri, 3/9) (solutions: polynomials, rationals)
- Homework 4 (due Mon, 2/27) [Some of these problems will be very challenging. Don't panic! Just spend some time trying to figure them out and turn in your best effort.] (solutions) [Solutions have been updated. The old version contained some mistakes.]
- Homework 3 (due Fri, 2/10) (solutions)
- Homework 2 (due Fri, 2/3) (solutions)
- Homework 1 (due Wed, 2/1) (solutions)
Practice problems (optional)
- Exams: 1 2 3
- Practice exam 3 (hints/partial solutions) [There was a typo in number 5. It should read 99/9]
- Trig graphs: 1-48 (from 5.3) and 1-52 (from 5.4) (solutions)
- Trig (radians): 1-12, 19-32 (from 5.1) and 1-36, 63-66 (from 5.2) (solutions)
- Trig (angles): 1-28 (solutions)
- Logarithmic functions: 1-32, 41-46 (from 4.1) and 1-56 (from 4.2) (solutions)
- Inverse functions 1-50 (solutions)
- Practice exam 2 (hints/partial solutions) [Note: the polynomial in problem 3(b) has degree 9!]
- Exponential functions: 5-24, 39-40, 42, 44 (solutions (odds))
- Rational functions: 5-56 (solutions (odds))
- Polynomial functions: 1-28, 65-70, 72 (solutions (odds))
- Practice exam 1 [The practice exam is longer than the real exam!] (solutions) [Some errors fixed!]
- Geometric Series (SRW 11.3): 39-46 (solutions)
- Arithmetic Series (SRW 11.2): 39-50, 53-56 (solutions)
- Series (SRW 11.1): 39-46, 53-66 (solutions)
- Geometric Sequences (SRW 11.3): 1-38 (solutions)
- Arithmetic Sequences (SRW 11.2): 1-38 (solutions)
- Sequences II (Stewart 11.1): 1-5, 13-18, 23-26, 28, 30-31, 33-34, 65, 69, 71
(solutions)
- Sequences I (SRW 11.1): 1-10, 23-30 (solutions)
- Functions II (Stewart 1.3): 1, 3, 4, 5, 29-46, 61, 62 (solutions)
- Functions I (Stewart 1.1): 3, 7, 9, 11, 13, 15, 25, 31-37, 39-49, 51-52
(solutions)
Class Schedule
- Wed, 5/2: Final review
- Mon, 4/30: Final review
- Fri, 4/27: Return and go over exam 3
- Wed, 4/25: Exam 3
- Mon, 4/23: Exam 3 review
- Fri, 4/20: Trig function graphs: phase shift. (See pg. 422-425 and 437-440 in SRW)
- Wed, 4/18: Amplitude and period (transformations) of trig functions (See pg. 422-425 and 437-440 in SRW)
- Mon, 4/16: Graphs of tan t, cot t, sec t, csc t (See pg. A30-A31 in Stewart) (See pg. 434-437 in SRW)
- Fri, 4/13: Graphs of sin t, cos t, tan t (See pg. A30-A31 in Stewart) (See pg. 418-419 and 434-436 in SRW)
- Wed, 4/11: Trig function values in the first quadrant. Graph of sin t (See pg. A30-A31 in Stewart) (See pg. 408-413 and 418-419 in SRW)
- Mon, 4/9: Trigonometric functions (or real numbers) sample problems (See pg. A24-A27 in Stewart) (See pg. 399-404 and 408-410 in SRW)
- Fri, 4/6: Unit cicle and terminal points. Trigonometric functions (or real numbers) (See pg. A24-A27 in Stewart) (See pg. 399-404 and 408-410 in SRW)
- Wed, 4/4: Trigonometric functions (of right triangles) (See pg. 478-481 in SRW)
- Mon, 4/2: Return and go over exam 2
- Fri, 3/30: Log functions: graphs, end behavior and properties (See pg. 62-64 in Stewart) (See pg. 343-344, 348-349 and 352-353 in SRW)
- Wed, 3/38: Inverse functions. Introduce log functions (See pg. 61-63 in Stewart) (See pg. 228-230 and 342 in SRW)
- Mon, 3/26: Inverse functions: how to find, horizontal line test, one-to-one test (See pg. 59-61 in Stewart) (See pg. 225-228 in SRW)
- Fri, 3/16: Exam 2.
- Wed, 3/14: Discuss practice exam 2 solutions.
- Mon, 3/12: End behavior and graphs of exponential functions. Begin exam 2 review. (See pg. 327-332 in SRW)
- Fri, 3/9: End behavior and graphs of exponential functions (See pg. 327-332 in SRW)
- Wed, 3/7: End behavior of rational functions. Introduce exponential functions (See pg. 299-309 and 327-329 in SRW)
- Mon, 3/5: More end behavior of rational functions (See pg. 299-309 in SRW)
- Fri, 3/2: Rational functions: end behavior and graphs (See pg. 299-309 in SRW)
- Wed, 2/29: How to graph polynomials: end behavior, x-intercepts, y-intercepts, intermediate behavior (See pg. 256-257 in SRW)
- Mon, 2/27: Polynomial functions: graphs and end behavior (See pg. 27-28 in Stewart) (See pg. 249-254 in SRW)
- Fri, 2/24: Return and go over exam 1
- Wed, 2/22: More representation of a repeating decimal as a rational. Proof that √2 is irrational. (See pg. A2 in Stewart) (See pg. 2-3 in SRW)
- Mon, 2/20: Number systems: naturals, integers, rationals, irrationals. Representation of a repeating decimal as a rational. (See A2 in Stewart) (See pg. 2-3 in SRW)
- Fri, 2/17: Exam 1.
- Wed, 2/15: Exam 1 review.
- Mon, 2/13: Infinite geometric series examples, Harmonic series. Begin review for exam 1 (See pg. 706, 708 in Stewart) (See pg. 843-844 in SRW)
- Fri, 2/10: More infinite sums, value infinite geometric series when -1 < r < 1 (See pg. 704-708 in Stewart) (See pg. 843-844 in SRW)
- Wed, 2/8: More on geometric series. Summation (sigma) notation, infinite sums, partial sums (See pg. 703-704 in Stewart) (See pg. 841-842 in SRW)
- Mon, 2/6: Arithmetic and geometric series. (See pg. 705 in Stewart) (See pg. 835-836, 838-841 in SRW)
- Fri, 2/3: More on limits of geometric sequences. Introduction to series. (See pg. 703-704 in Stewart) (See pg. 835-836 in SRW)
- Wed, 2/1: Limits of Arithmetic sequences. Geometric sequences and their limits. (See pg. 838-840 in SRW) (Limit laws for arithmetic and geometric sequences)
- Mon, 1/30: Limit laws for sequences. Rules for using infinity. Arithmetic sequences. (See pg. 833-834 in SRW)
- Fri, 1/27: More on formal definition of a limit of a sequence. Algebraic rules with limits. (See pg. 692-694 in Stewart)
- Wed, 1/25: Formal definition of limit of a sequence, bounded sequence. (See pg. 692-693 in Stewart) (See pg. 913-914 in SRW)
- Mon, 1/23: Translations of functions: Af(x+B)+C. Introduction to sequences, limits of sequence, increasing/decreasing sequences. (See pg. 689-691 in Stewart) (See pg. 173-174, 182-188, 821-824 in SRW)
- Fri, 1/20: Set-builder and interval notation. Graphs of equations and vertical line test. Increasing and decreasing functions. Idea of continuity. (See pg. 15, 19, A3-A4 in Stewart) (See pg. 157-166 in SRW)
- Wed, 1/18: Discuss class information. Review of functions, domain, range. (See pg. 9-15 in Stewart) (See pg. 147-154 in SRW)