Essential Mathematical Skills For Engineering Science and Applied Mathematics 1st Edition by S Barry ISBN 0868405655 9780868405650 by S Barry 9780868405650, 0868405655 instant download after payment.
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ISBN 10: 0868405655
ISBN 13: 9780868405650
Author: S Barry
Essential Mathematical Skills For Engineering Science and Applied Mathematics 1st Table of contents:
Part I: Core Algebraic and Pre-Calculus Skills
Chapter 1: Review of Fundamental Algebra
- A. Real Numbers and Operations: Integers, rational, irrational, real numbers.
- B. Algebraic Expressions: Simplification, factorization, expansion.
- C. Equations and Inequalities: Linear, quadratic, simultaneous equations.
- D. Functions and Graphs:
- Definition of a function, domain, range.
- Common functions: linear, quadratic, polynomial, rational.
- Graphing techniques, transformations.
Chapter 2: Essential Pre-Calculus Concepts
- A. Exponents and Logarithms: Laws of exponents, logarithmic properties, exponential and logarithmic functions.
- B. Trigonometry:
- Radian measure, unit circle.
- Trigonometric functions and identities.
- Solving trigonometric equations.
- Applications in geometry and physics.
- C. Complex Numbers:
- Basic operations, Argand diagram.
- Polar form, Euler's formula.
- De Moivre's Theorem.
Chapter 3: Vectors and Geometry
- A. Vector Algebra:
- Vectors in 2D and 3D.
- Addition, subtraction, scalar multiplication.
- Dot product, cross product, triple products.
- B. Lines and Planes in 3D Space.
- C. Coordinate Systems: Cartesian, polar, cylindrical, spherical.
Part II: Introduction to Calculus
Chapter 4: Differentiation
- A. Limits and Continuity.
- B. Definition of the Derivative: Geometric and physical interpretations.
- C. Rules of Differentiation: Power, product, quotient, chain rule.
- D. Derivatives of Elementary Functions: Polynomial, exponential, logarithmic, trigonometric.
- E. Higher Order Derivatives.
- F. Applications of Differentiation:
- Tangents and normals.
- Rates of change, optimization problems.
- Curve sketching.
Chapter 5: Integration
- A. Antiderivatives and Indefinite Integrals.
- B. The Definite Integral: Riemann sums, Fundamental Theorem of Calculus.
- C. Techniques of Integration:
- Substitution, integration by parts.
- Integration of rational functions (partial fractions).
- Trigonometric integrals.
- D. Improper Integrals.
- E. Applications of Integration:
- Area under a curve, volume of solids of revolution.
- Arc length, surface area.
- Work, average value of a function.
Chapter 6: Series and Sequences
- A. Sequences and Series: Convergence and Divergence.
- B. Taylor and Maclaurin Series:
- Approximating functions with polynomials.
- Common Maclaurin series.
- C. Fourier Series (Introduction):
- Representing periodic functions.
- Applications in signal processing.
Part III: Linear Algebra and Differential Equations
Chapter 7: Linear Algebra
- A. Matrices and Vectors:
- Matrix operations: addition, multiplication.
- Determinants and inverses.
- B. Solving Systems of Linear Equations:
- Gaussian elimination, Cramer's Rule.
- C. Vector Spaces and Subspaces.
- D. Eigenvalues and Eigenvectors:
- Importance in stability analysis, vibrations.
- E. Orthogonality and Projections.
Chapter 8: Ordinary Differential Equations (ODEs)
- A. Introduction to ODEs: Classification, order, linearity.
- B. First-Order ODEs:
- Separable, exact, linear, integrating factors.
- C. Second-Order Linear ODEs:
- Homogeneous equations with constant coefficients.
- Non-homogeneous equations (method of undetermined coefficients, variation of parameters).
- D. Systems of ODEs.
- E. Applications of ODEs:
- Growth and decay, oscillations, electrical circuits.
Part IV: Introduction to Multivariable Calculus and Further Topics
Chapter 9: Multivariable Calculus
- A. Functions of Several Variables:
- Partial derivatives.
- Chain rule for multivariable functions.
- B. Gradient, Divergence, Curl:
- Vector operators and their physical interpretations.
- C. Multiple Integrals:
- Double integrals, triple integrals.
- Change of variables (Jacobian).
- D. Vector Calculus (Introduction):
- Line integrals, surface integrals, volume integrals.
- Green's Theorem, Stokes' Theorem, Divergence Theorem.
Chapter 10: Probability and Statistics (Essential Concepts)
- A. Basic Probability Theory:
- Sample spaces, events, conditional probability.
- Random variables, probability distributions (discrete and continuous).
- B. Descriptive Statistics:
- Measures of central tendency and dispersion.
- C. Inferential Statistics (Brief Introduction):
- Hypothesis testing, confidence intervals.
- D. Regression and Correlation.
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