Math 3151 Calculus I

1. Syllabus – Semester I, 2023
2. Course Philosophy
3. Generic Course Objectives
4. Classroom Behaviour
5. On the use of electronic aparati
6. Recomendaciones para Estudiantes Nuevos
7. In Praise of Lectures

Calendar of Lectures – Weeks 1-15 with links to Course Page.

 

Week	Topics	Exercises
I	Review of Precalculus	Exercises
II	Limits  of sequences and functions	Exercises
II	Limits  of functions	Exercises
III	Continuity	Exercises
IV	The derivative	Exercises
EXAM I	Non Departmental	Practice
V	The derivative, Part II	Exercises
VI	Implicit differentiation, related rates	Exercises
VII	Logarithms	Exercises
EXAM II	Departmental	Practice
VIII	The Mean Value Theorem (MVT)	Exercises
IX	Optimization	Exercises
X	Antiderivatives	Exercises
XI	Antiderivatives Part II	Exercises
XII	The definite Integral	Exercises
XIII	The Fundamental Theorem of Calculus (FTC)	Exercises
XIII	Area under a curve	Exercises
EXAM III	Non Departmental	Practice
XIII	Volumes	Exercises
XIV	Logarithms in detail. Exponential functions	Exercises
	Exponential growth	Exercises
XV	Applications	Exercises
EXAM IV	Departmental

Review of Selected Precalculus Topics

Please read the following documents and practice the exercises therein.   Remember that each hour of  a math class requires at least  three hours of study.

1. On Definition (Definition according to Aristotle)
2. On Truth
3. On Implication.
4. On Validity
5. Review of Set Theory  and Predicate Logic
6. Section 1.1 of Santos‘ Precalculus Text.
7. Binary Relations and Functions <–Exercises Updated
8. Absolute Value 

Miscelleneous Calculus Notes

1. The Limit of a Sequence
2. The epsilon-delta definition of a limit -From Brilliant.org
3. Limits using Epsilon and Delta – Example.
4. Derivative of the Natural Logarithm
5. The Chain Rule
6. Points of Inflexion
7. Rates of Change
8. Rectilinear Motion
9. Mean Value Theorem
10. Optimization (Application to Optics)
11. Antiderivative Formulae
12. Substitution – more examples
13. Antiderivatives Involving the Secant Function
14. Telescoping Series
15. The Definite Integral
16. The Fundamental Theorem
17. First Mean Value Theorem for Integrals
18. Application of the FTC to Logarithms
19. Applications of the Definite Integral
20. Work
21. Harder Substitution Examples
22. The Irrationality of e

Text

George B. Thomas Jr. Maurice D. Weir, and Joel R. Hass, Calculus, 12th Edition.

Bibliography

1. K. Kodaira, (Editor), Basic Analysis, Japanese Grade 11. AMS
2. Y. M. Chow et. al., College Mathematics Volume 2, Syllabus C, Pan Pacific Publications, ISBN 9971-63-863-0.
3. Stewart and Tall, Foundations of Mathematics, Ed. 1, Oxford University Press.
4. Serge Lang, A First Course in Calculus, Addison Wesely, 1968.
5. Serge Lang, A Second Course in Calculus, Addison Wesely, 1968.
6. Salas, Hille y Anderson, Calculus, One and Several Variables, John Wiley.
7. Lecture Notes
8. (Free) Precalculus Book by David Santos
9. (Free) Ossifrage-And-Algebra-2007 by David Santos
10. (Free) Pre-y Cálculo Criollos (Spanish Version) by David Santos
11. (Free) Andragogic Propaedeutic Mathematics by David Santos
12. (Free) The Elements of Infinitesimal Calculus by David Santos
13. Michael Spivak, Calculus, Publish or Perish Inc., 1968.