Mathematics Course 1S3 for JF Science students
What is where in the textbook
Here is a guide to various textbooks where you can read in more detail about the course and find additional problems to practice on. This is now updated for the latest version (8th ed.) of the book by Anton, Bivens & Davis (the main textbook).
The largest part of the course is covered in Anton [1] . You are strongly recommended to get your own copy of this book. There are older editions in the library.
For Mathematica, there is a huge reference book by Wolfram [7] and there are some helpful remarks and exercises in Anton [1] .
For binary, octal and hexadecimal numbers there are chapters in some books in the library that cover more or less the right ground.
The probability and Statistics we do is covered in a book by Kreyszig [4] .
Course Contents
1 Binary, octal and hexadecimal numbers
2 Mathematica
3 Maxima and minima and graphing.
4 Integration
5 Techniques of integration
6 Applications of integration
7 Linear approximation and applications
8 An introduction to probability and statistics
References
1 Binary, octal and hexadecimal numbers
This topic is covered in Chapter 2 of [5] (510 M71 in the library) and Chapter 36 of [2] (510.24 L62*6 in the library). However, the notes available online here should suffice. At least in the new edition of [6], some of what we do is covered (on pages 51-67).
2 Mathematica
The Mathematica manual [7] by the inventor of Mathematica contains a lot more information about how to use the system than you need to know. The various handouts should provide most of the information you will need.
The online notes deal with approximately the same material as sections 1.1 to 1.9 of part 1 of the Mathematica book [7] . When you use the system, there is a "10 minute tutorial" you can run though that also covers most of the aspects we need.
In section 1.2 of Anton [1] , there is a general introduction to the way computer algebra systems are of use and one or two specific Mathematica examples. Throughout the book there are suggested exercises to do with computer algebra.
We discuss what parametric equations are (section 1.7 of Anton [1] ).
3 Maxima and minima and graphing.
Anton [1] , Chapter 4 (section 4.1-4.5) 2.
4 Integration
Anton [1] , Chapter 5, sections 1, 4-6.
5 Techniques of integration
Anton [1] , Chapter 8, sections 5-8. There is some mention of using computer algebra systems (including Mathematica). We take a slightly different view of numerical integration than in section 7.
6 Applications of integration
Anton [1] , Chapter 6, sections 1-4,6.
7 Linear approximation and applications
The references deal with linear approximation and Newton's method but not the bisection method or condition numbers.
Anton [1] , Chapter 3, section 9 and Chapter 4 section 6. The intermediate value theorem is in Chapter 2, section 5.
8 An introduction to probability and statistics
This material is covered in Kreyszig (7th edition) Chapter 23 sections 1, 2, and 4-7, and Chapter 24 section 4.
In the 8th edition [4] , the material is all in Chapter 22 (not including sections 4 and 9).
References
- [1]
- Howard Anton, Irl Bivens \& Stephen Davis, Calculus, 8th Edition, Wiley (2005)
- [2]
- Nelson Magor Cooke et al, Basic mathematics for electronics (7th edition), Glencoe, Lake Forest, Ill., 1992. [Hamilton 510.24 L62*6]
- [3]
- Ross L. Finney, Maurice D. Weir, Frank R. Giordano, & G. B. Thomas, Thomas' calculus Calculus and Analytic Geometry (10th edition), Addison Wesley, 2000. [Hamilton 515.1 K82*9;*, S-LEN 515.1 K82*9;* ]
- [4]
- Erwin Kreyszig, Advanced engineering mathematics (8th edition), Wiley, 1999 [Hamilton 510.24 L21*7]
- [5]
- Wilson T. Price, Charles Peselnick, Elements of data processing mathematics (3rd edition), Holt, Rinehart and Winston, 1987. [Hamilton 510 M71]
- [6]
- K. A. Stroud, Engineering Mathematics (6th ed), Palgrave Macmillan (2007).
- [6]
- Stephen Wolfram, Mathematica book, Wolfram Media and Cambridge University Press, 1999. [Hamilton 500.16424 N1999992*3]