SPRING 2025 - MATH 21B - ENGINEERING CALCULUS

Lecture: Eric Babson, babson@math.ucdavis.edu.
Mondays, Wednesdays and Fridays at 3:10 in California Hall.
Office: Mondays from 10:30 to 11:30 in 2109 Mathematical Sciences Building.
Sections:
B01: Kenton Ke on Tuesdays at 5:10 in 1020 Wickson Hall.
B02: Kenton Ke on Tuesdays at 6:10 in 207 Wellman Hall.
B03: Regina Zhou on Tuesdays at 5:10 in 140 Physics Building.
B04: Regina Zhou on Tuesdays at 6:10 in 217 Olson Hall.
B05: Soyeon Kim on Tuesdays at 7:10 in 207 Wellman Hall.
B06: Soyeon Kim on Tuesdays at 8:10 in 1132 Bainer Hall.
B07: Nathalie Ndigaya on Tuesdays at 6:10 in 140 Physics Building and in the calc room on Wednesdays from 5 to 6.
B08: Kaia Smith on Tuesdays at 7:10 in 3211 Teaching Learning Complex.
B09: Hadj Kerrouchi on Tuesdays at 7:10 in 130 Physics Building with office hours Tuesdays 5-6 and Fridays 4-5.

Calculus Room: Math 21ABCD Calculus Room , where TAs are available to answer your questions.

Text: Any calculus text, such as Thomas' Calculus: Early Transcendentals (13th+ edition).

Grades:: There will be 400 pts from 3 midterms and a final. One midterm will be dropped. The final will be half or a third of the grade - whichever is higher [more explicitly: The midterms will each have 100 points and the final will have 200 points. Your score will be the larger of (Ma+Mb+F) or (2/3)(2Ma+2Mb+F) where Ma and Mb are your two highest midterm scores.]

D-	D	D+	C-	C	C+	B-	B	B+	A-	A	A+
133	150	183	200	217	250	267	283	317	333	350	383

Homework: Problems are listed for each lecture and due at the end of the following week. They will not be collected. Nobody has ever learned mathematics without working out a great many exercises. If a section seems opaque work more similar problems. Problems are from the 14th edition of Thomas' Calculus: Sec 4.8 - 5.6, Sec 6.1 - 6.6, Sec 7.1 - 8.7 and Sec 8.8 - 11.4.

Answers: Answers to all odd problems from the previous edition. Thanks to Dr Kouba for the detailed solutions to these problems including those assigned from sections: 4.8, 5.1 and 5.2, 5.3, more 5.3 and 5.4, 5.5, 5.6, 6.1, 6.2, 6.3, 6.4, 6.5, more 6.5, 6.6, 7.1, 7.2, 8.1, 8.2, 8.3, 8.4, 8.5, 8.7, 8.8, 11.1, 11.2, 11.3 with six extra and 11.4.

Exams:
Midterm 1 Practice Midterm I and solutions.
Problems will be from chapter 5 topics including:
(1 problem) - Approximations of area or distance using rectangles and data from a function, table or graph. (Section 5.1)
(1 problem) - Summation evaluation either directly or via manipulation. (Section 5.2)
(1 problem) - Fundamental Theorem of Calculus I: derivatives of definite integrals. (Section 5.4)
(between 4 and 6 integrals involving)
- - Definite integrals:
- - - Area interpretation (Section 5.3)
- - - Average values (Section 5.3)
- - - Evaluation from given integrals using the rules (Section 5.3)
- - - Evaluation using geometry (eg parts of circles or triangles) (Section 5.3)
- - - Fundamental Theorem of Calculus II: evaluation using indefinite integrals (Section 5.4) and substitution (Section 5.6)
- - Indefinite Integrals: Antiderivatives... remember the constant of integration +C. (Section 5.5)
- - - Powers, Trigonometric functions, Exponential and Ln functions (21A and Section 5.5)
- - - Substitution (Sections 5.5 and 5.6).
(1 extra credit problem)

This table of integrals will appear on the exam cover.

Course Outline: The focus of MAT 21B is on integration. The relationship between differentiation (MAT 21A) and integration is the Fundamental Thoerem of Calculus which continues after three centuries to have enormous impact in engineering, science and mathematics. After defining integrals and discussing the fundamental theorem this course will look at some methods for computing integrals. Despite their close link integrals turn out to be much harder to find than derivatives. The course will then cover a range of applications.