Author | Marshall, Gordon S. author |
---|---|
Title | Introductory Mathematics: Applications and Methods [electronic resource] / by Gordon S. Marshall |
Imprint | London : Springer London, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-3412-1 |
Descript | IX, 226 p. online resource |
1. Simultaneous Linear Equations -- 1.1 Introduction -- 1.2 The method of determinants -- 1.3 Gaussian elimination -- 1.4 Ill-conditioning -- 1.5 Matrices -- 2. Vector Algebra -- 2.1 Introduction -- 2.2 Algebraic representation -- 2.3 Linear independence -- 2.4 The scalar product -- 2.5 The vector product -- 2.6 Triple products -- 2.7 Differentiation of vector functions -- 3. Complex Numbers -- 3.1 Introduction -- 3.2 Algebra of complex numbers -- 3.3 Graphical representation -- 3.4 Polar form -- 3.5 Exponential form -- 3.6 De Moivreโs theorem -- 4. Review of Differentiation Techniques -- 4.1 Introduction -- 4.2 Differentiation of standard functions, -- 4.3 Function of a function -- 4.4 The product rule -- 4.5 The quotient rule -- 4.6 Higher derivatives -- 4.7 Implicit differentiation -- 4.8 Logarithmic differentiation -- 5. Review of Integration Techniques -- 5.1 Introduction -- 5.2 Integration of standard functions -- 5.3 Integration by substitution -- 5.4 Integration using partial fractions -- 5.5 Integration by parts -- 6. Applications of Differentiation -- 6.1 Introduction -- 6.2 Functions: -- 6.3 Curve sketching -- 6.4 Optimisation -- 6.5 Taylor series -- 7. Partial Differentiation -- 7.1 Introduction -- 7.2 Notation -- 7.3 Total differentials -- 7.4 The total derivative -- 7.5 Taylor series for functions of two variables -- 7.6 Maxima, minima and saddlepoints -- 7.7 Problems with constraints: -- 7.8 Lagrange multipliers -- 8. Multiple Integrals -- 8.1 Double integrais -- 8.2 Triple integrais -- 9. Differential Equations -- 9.1 Introduction -- 9.2 First order differential equations -- 9.3 Second order equations -- Solutions to Exercises