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1. Computers, Science, and Engineering 2. Infinite Series 3. Complex Numbers and Functions 4. Vectors and Matrices 5. Matrix Transformations 6. Multidimensional Problems 7. Vector Analysis 8. Tensor Analysis 9. Gamma Function 10. Ordinary Differential Equations 11. General Vector Spaces 12. Fourier Series 13. Integral Transforms 14. Series Solutions: Important ODEs 14. General Vector Spaces 15. Partial Differential Equations 16. Calculus of Variations 17. Complex Variable Theory 18. Probability and Statistics Appendix A Methods for Making Plots Appendix B Printing Tables of Function Values Appendix C Data Structures for Symbolic Computing Appendix D Symbolic Computing of Recurrences Formulas Appendix E Partial Fractions Appendix F Mathematical Induction Appendix G Constrained Extrema Appendix H Symbolic Computing for Vector Analysis Appendix I Maple Tensor Utilities Appendix J Wronskians in ODE Theory Appendix K Maple Code for Associated Legendre Functions and Spherical Harmonics Index