Preparing for Calculus I: Essential Topics & Recommended Books

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The discussion centers around preparing for Calculus I and II as part of a Computer Engineering program. The participant expresses concern about their math background, particularly in topics like limits and derivatives, which are crucial for success in calculus. The objectives for Calculus I include learning mathematical analysis techniques applicable to physics, chemistry, and engineering, along with developing logical reasoning skills. Recommended textbooks include "Calculus" by Anton, Bivens, and Davis, which is considered a suitable starting point for beginners. Other suggested resources are texts by Swokowski, Salas, Apostol, and Stewart, but Anton is favored for its accessibility. The program covers essential topics such as sequences, limits, continuity, differentiability, applications of derivatives, integrals, and properties of various functions. Overall, the emphasis is on mastering calculus fundamentals to build a solid foundation for future studies.
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Hello to all , first of all sorry for my poor english.
So this year I made the final exams and got accept to go to University to take Computer Engeneer I don't know if that's what is called on there , despite my bad math formation I did it.
Now I will have Calcuclus I and II and I have to prepare my self becouse I am suppose to already know some stuff for calculus that I wasnt tought like limits and derivate.

These are the objectives for Calculus I :

Learn the basic topics of Mathematical Analysis. It is intended that the students acquire elementary techniques of calculus for the Physics, Chemistry and Engineering. Moreover, they should develop solid methods of logical reasoning.

The are the books used and recommend:

Main book -Anton, Bivens, Davis - Calculus, 8th Edition, Wiley, 2005 .

Other:

1. Cálculo com geometria analítica, Earl W. Swokowski, MacGraw-Hill,1983.
2. SALAS, HILLE - Calculus, one and several variables, John Wiley Sons, Inc, 1995.
3. APOSTOL, T. - Calculus, Blaisdell, 1967.
4. CAMPOS FERREIRA, J. - Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1982.
5. STEWART, J. - Calculus, 3ª edição, Brooks/Cole Publishing Company, 1995.


This is the program:

1-Sequences of real numbers (main results)
2-Real functions of a real variable: limits and continuity
2.1 Definition of limit
2.2 Properties of limits
2.3 Lateral limits
2.4 Continuity
3- Differentiability of real functions of a real variable
3.5 Definition of derivatives
3.6 Derivation rules
3.7 Derivative of composition of functions
3.8 Derivatives of higher order
4- Applications of the derivative
4.1 Local extrema
4.2 Rolle and Lagrange''''''''s theorems
4.3 Concavity and asymptotes
4.4 Anti derivatives
5- Integral
5.1 Definition of integral
5.2 Properties of integral
5.3 Mean value theorem
5.4 The fundamental theorem of calculus
5.5 Change of variables
5.6 Integration by parts
6- Logarithmic, exponential, and trigonometric functions and their properties
7- Indeterminate forms and L´Hôpital''''''''s rule
8- Improper integrals
9- Taylor''''''''s formula
10- Sequences of real numbers


My math is on really bad shap I really want to master it so based on this would you recommend the Main book -Anton, Bivens, Davis - Calculus, 8th Edition, Wiley, 2005 ?
 
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I know someone who is using Anton right now and she says it's a decent book. It is probably very similar to the Salas text and the Stewart text. Apostol will be more difficult and probably not necessary. You should be fine with Anton.
 
So what book do you suggest to start learning calculus easly ?
 
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