Meeting the needs of scientists - whether mathematicians, physicists, chemists or engineers --in terms of symbolic computation, this book allows them to quickly locate the method they require for the precise problem they are adressing. It requires no prior experience of symbolic computation, nor specialized mathematical knowledge, and provides quick access to the practical use of symbolic computation software. The organization of the book in mutually independent chapters, each focusing on a specific topic, allows the user to select what is of interest without necessarily reading everything and the whole is supplemented by a detailed table of contents and index,.

1. What MAPLE Can Do for You.- 1.1 Arithmetic.- 1.2 Numerical Computations.- 1.3 Polynomials and Rational Functions.- 1.4 Trigonometry.- 1.5 Differentiation.- 1.6 Truncated Series Expansions.- 1.7 Differential Equations and Systems.- 1.8 Integration.- 1.9 Plot of Curves.- 1.10 Plot of Surfaces.- 1.11 Linear Algebra.- 2. Introduction.- 2.1 First Steps.- 2.1.1 Keyboarding an Expression.- 2.1.2 Operators, Functions and Constants.- 2.1.3 First Computations.- 2.2 Assignment and Evaluation.- 2.2.2 Identifiers.- 2.2.3 Assignment.- 2.2.4 Free Variables and Evaluation.- 2.2.5 Full Evaluation Rule.- 2.2.6 Use of Apostrophes: Partial Evaluation.- 2.3 Evaluation of Function Arguments.- 2.3.1 Fundamental Operations.- 2.3.2 The Function expand.- 2.3.3 The Function factor.- 2.3.4 The Function normal.- 2.3.5 The Function convert in Trigonometry.- 2.3.6 First Approach to the Function simplify.- 2.3.7 Simplification of Radicals: radnormal and rationalize.- 2.3.8 The Functions collect and sort.- 2.4 First Approach to Functions.- 2.4.1 Functions of One Variable.- 2.4.2 Functions of Several Variables.- 2.4.3 The Difference Between Functions and Expressions.- 2.4.4 Links Between Expressions and Functions.- 2.5 Simplification of Power Functions.- 2.5.1 The Functions exp, In and the Exponentiation Operator.- 2.5.2 The Function simplify.- 2.5.3 The Function combine.- 3. Arithmetic.- 3.1 Divisibility.- 3.1.1 Quotient and Remainder.- 3.1.2 G.c.d. and Euclid's Algorithm.- 3.1.3 Decomposition into Prime Factors.- 3.1.4 Congruences.- 3.2 Diophantian Equations.- 3.2.1 Chinese Remainder Theorem.- 3.2.2 Solution of Equations Modulo n.- 3.2.3 Classical Equations.- 4. Real Numbers, Complex Numbers.- 4.1 The Real Numbers.- 4.1.1 Display of Real Numbers.- 4.1.2 Approximate Decimal Value of Real Numbers.- 4.2 The Complex Numbers.- 4.2.1 The Different Types of Complex Numbers.- 4.2.2 Algebraic Form of the Complex Numbers.- 4.2.3 Trigonometric Form of the Complex Numbers.- 4.2.4 Computing with Expressions with Complex Coefficients.- 4.2.5 Approximate Decimal Value of the Complex Numbers.- 5.1 Curves Defined by an Equation y = f (x).- 5.1.1 Graphic Representation of an Expression.- 5.1.2 Graphic Representation of a Function.- 5.1.3 Simultaneous Plot of Several Curves.- 5.1.4 Plot of a Family of Curves.- 5.2 The Environment of plot.- 5.2.1 The plot Menu in Windows.- 5.2.2 The Options of plot.- 5.3 Parametrized Curves in Cartesian Coordinates.- 5.3.1 Plot of a Parametrized Curve.- 5.3.2 Simultaneous Plot of Several Parametrized Curves.- 5.3.3 Plot of a Family of Parametrized Curves.- 5.4 Curves in Polar Coordinates.- 5.4.1 Plot of a Curve in Polar Coordinates.- 5.4.2 Plot of a Family of Curves in Polar Coordinates.- 5.5 Curves Defined Implicitly.- 5.5.1 Plot of a Curve Defined Implicitly.- 5.5.2 Plot of a Family of Implicit Curves.- 5.5.3 Precision of the Plot of Implicit Curves.- 5.6 Polygonal Plots.- 5.7 Mixing Drawings.- 5.7.1 How Does plot Work.- 5.7.2 The Function display.- 5.8 Animation.- 5.9 Using Logarithmic Scales.- 6. Equations and Inequations.- 6.1 Symbolic Solution: solve.- 6.1.1 Univariate Polynomial Equations.- 6.1.2 Other Equations in One Variable.- 6.1.3 Systems of Equations.- 6.1.4 Inequations.- 6.2 Approximate Solution of Equations: fsolve.- 6.2.1 Algebraic Equations in One Variable.- 6.2.2 Other Equations in One Variable.- 6.2.3 Systems of Equations.- 6.3 Solution of Recurrences: rsolve.- 6.3.1 Linear Recurrences.- 6.3.2 Homographic Recurrences.- 6.3.3 Other Recurrence Relations.- 7. Limits and Derivatives.- 7.1 Limits.- 7.1.1 Limit of Expressions.- 7.1.2 Limit of Expressions Depending on Parameters.- 7.1.3 Limit of Functions.- 7.2 Derivatives.- 7.2.1 Derivatives of Expressions in a Single Variable.- 7.2.2 Partial Derivatives of Expressions in Several Variables.- 7.2.3 Derivatives of Functions in One Variable.- 7.2.4 Partial Derivatives of Functions in Several Variables.- 8. Truncated Series Expansions.- 8.1 The Function series.- 8.1.1 Obtaining Truncated Series Expansions.- 8.1.2 Generalized Series Expansions.- 8.1.3 Regular Part of a Series Expansion.- 8.1.4 Obtaining an Equivalent.- 8.1.5 Limits of the Function series.- 8.2 Operations on Truncated Series Expansions.- 8.2.1 Sums, Quotients, Products of Truncated Series Expansions.- 8.2.2 Compositions and Inverses of Truncated Series Expansions.- 8.2.3 Integration of a Truncated Series Expansion.- 8.3 Series Expansion of an Implicit Function.- 9. Differential Equations.- 9.1 Methods for Solving Exactly.- 9.1.1 Differential Equations of Order 1.- 9.1.2 Differential Equations of Higher Order.- 9.1.3 Classical Equations.- 9.1.4 Systems of Differential Equations.- 9.2 Methods for Approximate Solutions.- 9.2.1 Numerical Solution of an Equation of Order 1.- 9.2.2 Numerical Solution of an Equation of Higher Order.- 9.2.3 Computing a Truncated Series Expansion of the Solution.- 9.3 Methods to Solve Graphically.- 9.3.1 Differential Equation of Order 1.- 9.3.2 The Options of DEplot for a Differential Equation.- 9.3.3 Differential Equation of Order n.- 9.3.4 Necessity of the Option stepsize.- 9.3.5 Differential System of Order 1.- 9.3.6 Study of an Example.- 10. Integration and Summation.- 10.1 Integration.- 10.1.1 Exact Computation of Definite and Indefinite Integrals.- 10.1.2 Generalized Integrals.- 10.1.3 Inert Form Int.- 10.1.4 Numerical Evaluation of Integrals.- 10.2 Operations on Unevaluated Integrals.- 10.2.1 Integration by Parts.- 10.2.2 Variable Substitution in an Integral.- 10.2.3 Differentiation Under the Integral Sign.- 10.2.4 Truncated Series Expansion of an Indefinite Integral.- 10.3 Discrete Summation.- 10.3.1 Indefinite Sums.- 10.3.2 Finite Sums.- 11. Three-Dimensional Graphics.- 11.1 Surfaces Defined by an Equation z = f (x, y).- 11.1.1 Plot of a Surface Defined by an Expression.- 11.1.2 Plot of a Surface Defined by a Function.- 11.1.3 Simultaneous Plot of Several Surfaces.- 11.2 The Environment of plot3d.- 11.2.1 The Menu of plot3d in Windows.- 11.2.2 The Options of plot3d.- 11.3 Surface Patches Parametrized in Cartesian Coordinates.- 11.4 Surfaces Patches Parametrized in Cylindrical Coordinates.- 11.5 Surface Patches Parametrized in Spherical Coordinates.- 11.6 Parametrized Space Curves.- 11.6.1 Plot of a Parametrized Curve.- 11.6.2 Simultaneous Plot of Several Parametrized Curves.- 11.7 Surfaces Defined Implicitly.- 11.8 Mixing Plots from Different Origins.- 12. Polynomials with Rational Coefficients.- 12.1 Writing Polynomials.- 12.1.1 Reminders: collect, sort, expand.- 12.1.2 Indeterminates of a Polynomial.- 12.1.3 Value of a Polynomial at a Point.- 12.2 Coefficients of a Polynomial.- 12.2.1 Degree and Low Degree.- 12.2.2 Obtaining the Coefficients.- 12.3 Divisibility.- 12.3.1 The Function divide.- 12.3.2 Euclidean Division.- 12.3.3 Resultant and Discriminant.- 12.4 Computation of the g.c.d. and the I.c.m.- 12.4.1 The Functions gcd and lem.- 12.4.2 Content and Primitive Part.- 12.4.3 Extended Euclid's Algorithm: The Function gcdex.- 12.5 Factorization.- 12.5.1 Decomposition into Irreducible Factors.- 12.5.2 Square-Free Factorization.- 12.5.3 Irreducibility Test.- 13. Polynomials with Irrational Coefficients.- 13.1 Algebraic Extensions of ?.- 13.1.1 Irreducibility Test.- 13.1.2 Roots of a Polynomial.- 13.1.3 The Fun…