f19_math150H

Honors Calculus I

- Fall 2019 -

Instructor: Kwangho Choiy

• Office: Neckers 283 (618-453-6508)

• E-mail: kchoiy_at_siu_dot_edu 

• Office Hours: MonWedFri 9-10am; 12-1pm, or by appointment. Emails are also available.

Course Website: https://sites.google.com/site/kchoiy/home/teaching/f19_math150H

Class Meeting: MonWedThrFri 11:00am - 11:50am in EGRA 422 

Textbook: Essential Calculus: Early Transcendentals, 2nd edition by James Stewart (ISBN:9781133112280). 

Objectives/Topics: Our goal is to learn major concepts and techniques of single variable calculus. The topics include: fundamental concepts, proofs, epsilon-delta, computations, techniques, and applications of limits, continuity, and derivatives, Newton’s method, Riemann sums, differential equations, and some of: the Trapezoidal rule or Simpson's rule, definition and applications of definite integrals. ♯ We will cover Section 1.1–1.6, 2.1–2.8, 3.1–3.3, *3.4, 3.5, 3.6, 4.1–4.6, *4.7, 5.1–5.5, 7.1–7.3, *7.6, *7.7 (*= tba in due course whether to cover). Our tentative class schedule is available on Syllabus linked below.

Syllabus / Course Schedule: It is required to read carefully our syllabus and schedule linked [here], updated on Aug. 15, 2019.

Exams: There will be three mid-term exams and one final in our classroom EGRA 422.

1.  Exam 1 (in class on 9/6, Fri) covers Sections 1.1-1.5 (intermediate value theorem is excluded) prac problms

2.  Exam 2 (in class on 10/11, Fri) covers Sections 1.5(Only the intermediate value theorem), 1.6, 2.1-2.8, 3.1-3.3 prac problms

3.  Exam 3 (in class on 11/13, Wed) covers Sections 3.5, 3.6, 4.1, 4.3-4.7, 5.3, 5.5 prac problms

4.  Final Exam (10:15am-12:15pm on Dec 13, Friday, at our classroom) will be comprehensive: approximately, 40% on Sections 1.1-1.6, 2.1-2.8, 3.1-3.3, 3.5, 3.6, 4.1, 4.3-4.7, 5.3, 5.5, and 60% on Sections 4.2, 7.1-7.3. prac problms

Project: One project with presentation per student will be given. More details will be discussed in due course.

Quizzes: Each quiz will be generally taken in class on a weekly basis, otherwise will be announced in due course before the date (**Refer to Syllabus linked above for a tentative Quiz schedule). Quizzes are from Worksheets which are distributed a week ahead of time in class as well as liked below. *Quiz Policies are written in the syllabus and each Worksheet.

1. Quiz 1 (scheduled for 8/23, Fri) from Worksheet 1 

2. Quiz 2 (scheduled for 8/30, Fri) from Worksheet 2 

3. Quiz 3 (scheduled for 9/16, Mon) from Worksheet 3

4. Quiz 4 (scheduled for 9/23, Mon) from Worksheet 4

5. Quiz 5 (scheduled for 9/30, Mon) from Worksheet 5

6. Quiz 6 (scheduled for 10/7, Mon) form Worksheet 6

7. Quiz 7 (scheduled for 10/21, Mon) from Worksheet 7

8. Quiz 8 (scheduled for 10/28, Mon) from Worksheet 8

9. Quiz 9 (scheduled for 11/4, Mon) from Worksheet 9

10. Quiz 10 (scheduled for 11/22, Fri) from Worksheet 10

Tutoring Information: Visit at this department website.

Updates and Remarks - MATH150H - Fall 2019:

[Dec,6] Review Session for Final Exam / Sec 7.7 quick introduction to differential equations, separation, how to solve it.

[Dec,5] Review Session for Final Exam.

[Dec,4] Two students' Presentations. / Final Exam announced at D2L as well,  prac problms handed out by E-mail & at D2L.

[Dec,2] Sec 5.1 Revisited a general form of Riemann sum including mid-point rule, upper sum, lower sum. Student' Presentation / Graded Quiz 10 returned. / Final Exam announced by email.

[Nov,22] Sec 7.1 -7.3 shell method, examples. Quiz 10 taken, its solution distributed.

[Nov,21] Sec 7.1 -7.3 more examples for volume, dx, dy, motive for shell method.

[Nov,20] Sec 7.1 -7.3 more examples, tips for integral and area, volume. Student' Presentation / Graded Exam 3 returned with solution.

[Nov,18] Sec 7.1 -7.3 integral and area, volume, example.  Worksheet 10 for Quiz 10(scheduled for 11/22, Fri) is emailed on 11/16, handed out.

[Nov,13] Exam 3 taken.

[Nov,8] Review session for Exam 3. Helpful note&partial solutions to Prac.Problm for Exam 3 emailed.

[Nov,7] Sec 5.4, 4.2 - proof of mvt using extreme value theorem, Rolle’s theorem / Review session for Exam 3 

[Nov,6] Sec 5.4, 4.2 - introduced another version of Fundamental theorem of calculus, Mean value theorem, meaning, examples. proved FTC.

[Nov,5] Sec 5.1,5.2,5.4 - Proof of Fundamental theorem of calculus. Graded Quiz 9 returned./ Exam 3 announced by email,D2L as well, prac problms handed out.

[Nov,4] Sec 5.1,5.2,5.4 - Riemann sum and definite integral, Fundamental theorem of calculus, examples. Quiz 9 taken, its solution distributed.

[Nov,1] Sec 5.1,5.2,5.4 - Riemann sum, concept, motive, example, remarks. 

[Oct,31] Sec 4.7,5.3, 5.5 - integration by substitution, motivation, examples. Helpful note&partial solutions to Worksheet 9 emailed.

[Oct,30] Sec 4.7,5.3, 5.5 - listed all formulae, further techniques for integrals, examples.

[Oct,29] Sec 4.7,5.3, 5.5 - indefinite integral, definite integral, notations, motivating examples, remarks. Graded Quiz 8 returned.

[Oct,28] Sec 4.6 - gave all steps of Newton's method, formula for x_n+1 and x_n, examples. Worksheet 9 for Quiz 9(scheduled for 11/4, Mon) is handed out / Quiz 8 taken, its solution distributed.

[Oct,25] Sec 4.1,4.3-4.6 examples for graphing, word problems / Sec 4.6 - introduced Newton's method, motivating example, the method.

[Oct,24] Sec 4.1,4.3-4.6 examples, graphing with f', f'', x-intercept, y-intercept, symmetric information i.e., even, odd,  limits. Helpful note&partial solutions to Worksheet 8 emailed.

[Oct,23] Sec 4.1,4.3-4.6 more examples for increasing decreasing, local min/max, absolute min/max, concave up/down. Introduced limit usage for graphing. Graded Quiz 7 returned.

[Oct,21] Sec 4.1,4.3-4.6 more graph-related example for global(absolute) min/max, critical numbers, local min/max, 2nd derivative test, concave up&down and f''(x),  f''>0 =>  f' increasing => f is convcave up /  f''<0 =>  f' decreasing => f is convcave down, inflation points. Worksheet 8 for Quiz 8(scheduled for 10/28, Mon) is handed out / Quiz 7 taken, its solution distributed.

[Oct,18] Sec 4.1,4.3-4.6 global(absolute) min/max, strategy to get them, critical numbers, local min/max, strategy to get them, examples. 

[Oct,17] Sec 3.5-3.6 properties, proofs of a^x, log_a(x), examples / Sec 4.1 motivations, main rough tool, examples.

[Oct,16] Sec 3.5-3.6 derivative of arccos, arctan, with proofs, examples, a^x, log_a(x), their graphs, derivatives.

[Oct,14] Sec 3.5-3.6 introduced arcsin, arccos, arctan, with domain and range, graphs, examples to evaluate, derivative of arcsin with proof. Worksheet 7 for Quiz 7(scheduled for 10/21, Mon) is handed out / Graded Exam 2 returned with solution.

[Oct,11] Exam 2 taken. Exam 2 solution emailed

[Oct,10] Review session for Exam 2. 

[Oct,9] Review session for Exam 2. Graded Quiz 6 returned.

[Oct,7] Sec 3.3-3.6 more examples/techniques for derivatives and limits regarding e^x, lnx. Quiz 6 taken, its solution distributed.

[Oct,4] Sec 3.3-3.6 examples for (f^{-1})’(x)=f’(f^{-1}(x)), derivative of e^x, lnx, and their proofs, limit-related examples with e^x, lnx, implicit diff taking ln x both sides. Exam 2 announced by email,D2L as well, prac problms handed out / helpful note&partial solutions to Worksheet 6 emailed.

[Oct,3] Sec 3.3-3.6 proof (f^{-1})’(x)=f’(f^{-1}(x)), described def, graph, properties of e^x, lnx, examples.

[Oct,2] Sec 3.3-3.6 more examples for inverse functions, bijective functions, technique to get the inverse, examples, domain, range of the inverse function, (f^{-1})^{-1}=f, introduce lnx, and its graph using the notion of inverse functions. Graded Quiz 5 returned.

[Sep,30] Sec 3.1-3.2 more examples for inverse functions, injective(1-1), surjective(onto), bijective functions, f^{-1} exists iff f(x) is bijective, strategy to get f^{-1}, geometric relationship (reflective wrt y=x) between f and f^{-1}. Worksheet 6 for Quiz 6(scheduled for 10/7, Mon) is handed out / Quiz 5 taken, its solution distributed.

[Sep,27] Sec 3.1-3.2 identity function I(x)=x for all x, domain=codomain=range, definition of the inverse function, notation y=f^{-1}(x), example, question when f^{-1} exists or when not, additionally introduced concept of identity/inverse elements with respect to a given operation in an algebraic structure.

[Sep,25] Sec 2.6-2.8 one more word problem / Sec 3.1-3.2 motivating example for inverse function, gave definitions of e, y=e^x, graph, examples.

[Sep,25] Sec 2.6-2.8 linear approximation, examples, word problems, typical strategy, example.

[Sep,23] Sec 2.6-2.8 more examples for implicit differentiation. Worksheet 5 for Quiz 5(scheduled for 9/30, Mon) is handed out / Quiz 4 taken, its solution distributed.

[Sep,20] Sec 2.6-2.8 proved that f(x)=|x| is not differentiable at x=0, continuous <= differentiable, but not the reverse with counterexample, introduce higher derivatievs, introduced dy/dx and rewrote the chain rule, implicit differentiation, examples.

[Sep,19] Sec 2.3-2.5 example requiring a combination of all derivative formulae / Sec 2.6-2.8 f'(x)>0 => f(x) increases,  f'(x)<0 => f(x) decreases, differentiable, examples,  

[Sep,18] Sec 2.3-2.5 (f+-g)', product rule, quotient rule, chain rule, and their proof, examples . Graded Quiz 3 returned.

[Sep,16] Sec 2.3-2.5 (cosx)'=- sinx, listed upcoming derivative formulae . Worksheet 4 for Quiz 4(scheduled for 9/23, Mon) is handed out / Quiz 3 taken, its solution distributed.

[Sep,13] Sec 2.3-2.5 proved of (x^n)'=nx^(n-1), introduced and proved (sinx)'=cosx, (constant)'=0.

[Sep,12] Sec 2.1-2.2 another type of definition of derivative, f'(x), derivative as function, more examples, equation of tangent line / Sec 2.3-2.5 (x^n)'=nx^(n-1).

[Sep,11] Sec 1.5-1.6 more examples for proving a limit involving infinity and for proving the existence of solution using IVT / Sec 2.1-2.2 motivation of derivatives, defined f'(a), the derivative of f(x) at x=a, whose meaning is the slope of the tangent line at x=a.

[Sep,10] Sec 1.5-1.6 more examples for limit involving infinity, 4 definitions of limit involving infinity towards proof, IVT, examples. Graded Exam 1 returned; solution Emailed.

[Sep,9] Sec 1.6 limit involving infinity, concepts and two techniques, examples. Worksheet 3 for Quiz 3(scheduled for 9/16, Mon) is handed out.

[Sep,6] Exam 1 taken.

[Aug,30] Sec 1.3-1.5 more example for epsilon-delta definition, defined continuity using limit, limx->af(x)=f(a), example.  Exam 1 announced by email,D2L as well, prac problms handed out / Quiz 2 taken, its solution distributed.

[Aug,29] Sec 1.3-1.5 f(x)->L <=> distance getting to 0 <=> |f(x)-L|< epsilon for any arbitrary epsilon >0, epsilon-delta definition (method), proof related to proof.

[Aug,28] Sec 1.3-1.5 squeeze lemma(theorem) with showing lim_x->0(sinx)/x=1, finalized three main techniques to evaluation limits, examples, addition, subtraction, multiplication, division of continuous functions

[Aug,27] Sec 1.3-1.5 more about techniques to evaluate limits for continuous cases, cancellation technique, examples, some useful statements

[Aug,26] Sec 1.3-1.5 introduced concepts of infinity and limit, some remarks on limits, examples, left limit, right limit, DNE, a technique to get a limit using continuity in a graph. Returned graded Quiz 1.

[Aug,23] Sec 1.1-1.2 more examples of functions, transformations, function compositions. Quiz 1 taken, its solution distributed / Worksheet 2 for Quiz 2(scheduled for 8/30, Fri) is handed out.

[Aug,22] Sec 1.1-1.2 get functions from equations, two techniques, graph, shifting graphs, examples. Hand-Out I for further kinds of functions and graphs distributed/ partial solutions to Worksheet 1 emailed.  

[Aug,21] Sec 1.1-1.2 terminologies related to functions, domain, codomain, range, image, pre-image, equations, polynomials, circles, N, Z, Q, R.

[Aug,19] Syllabus with project topics has been distributed in class, discussed syllabus, objectives - function, limit, derivative, integral / Sec 1.1-1.2 Gave a definition of a function, example and counter examples. Worksheet 1 for Quiz 1(scheduled for 8/23, Fri) is handed out.

[Aug,15] Syllabus and Worksheet 1 are uploaded as above in PDF as well as D2L.