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This book aims to provide a basic and self-contained introduction to Applied Mathematics within a computational environment. The book is aimed at practitioners and researchers interested in modelling real world applications and verifying the results.
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This book aims to provide a basic and self-contained introduction to Applied Mathematics within a computational environment. The book is aimed at practitioners and researchers interested in modelling real world applications and verifying the results.
Produktdetails
- Produktdetails
- Verlag: Taylor & Francis Ltd
- Seitenzahl: 322
- Erscheinungstermin: 18. September 2024
- Englisch
- Abmessung: 234mm x 156mm
- ISBN-13: 9781032595245
- ISBN-10: 1032595248
- Artikelnr.: 70146722
- Verlag: Taylor & Francis Ltd
- Seitenzahl: 322
- Erscheinungstermin: 18. September 2024
- Englisch
- Abmessung: 234mm x 156mm
- ISBN-13: 9781032595245
- ISBN-10: 1032595248
- Artikelnr.: 70146722
João Luís de Miranda is currently a Professor at ESTG-Escola Superior de Tecnologia e Gestão (IPPortalegre) and a Researcher in Optimization methods and Process Systems Engineering (PSE) at CERENA-Centro de Recursos Naturais e Ambiente (IST/ULisboa). He has been teaching for more than 25 years in the field of Mathematics (e.g., Calculus, Operations Research-OR, Management Science-MS, Numerical Methods, Quantitative Methods, Statistics) and has authored/edited several publications in Optimization, PSE, and education subjects in engineering and OR/MS contexts. João Luís de Miranda is addressing the research subjects through international cooperation in multidisciplinary frameworks, and is currently serving on several boards/committees at national and European level.
1. First Notes on Real Functions. 1.1. Introduction. 1.2. A Function of
Real Numbers. 1.3. The Cost Function. 1.4. Function Representation in Table
and Graphic. 1.5. Proofs and Mathematical Reasoning. 1.6. The Inverse
Rationale. 1.7. Discussion of Results. 1.8. Concluding Remarks. 2.
Sequences of Real Numbers. 2.1. Introduction. 2.2. Preliminary Notions.
2.3. Limit and Convergence of a Sequence. 2.4. Theorems About Sequences.
2.5. Study of Important Sequences. 2.6. Notes on Numbers Computation. 2.7.
Concluding Remarks. 3. Limit of a Function. 3.1. Introduction. 3.2. Notions
About Function Limits. 3.3. Lateral Limits at a Point - the Extended Cost
Function. 3.4. Properties of Function Limits. 3.5. Remarkable Limits. 3.6.
Concluding Remarks. 4. Continuity. 4.1. Introduction. 4.2. Continuity at a
Point. 4.3. Continuity on a Range. 4.4. Properties of Continuous Functions.
4.5. Theorems about Continuous Functions. 4.6. Roots of Non-linear
Equations. 4.7. Concluding Remarks. 5. Derivative of a Function. 5.1.
Introduction. 5.2. Derivatives and Geometric Interpretation. 5.3.
Derivation Rules. 5.4. Derivation of Important Functions. 5.5. Derivative
of Inverse Function. 5.6. Derivatives of Different Orders. 5.7. Concluding
Remarks. 6. Sketching Functions and Important Theorems. 6.1. Introduction.
6.2. Important Theorems on Differentiable Functions. 6.3. Maxima and
Minima. 6.4. Asymptotes. 6.5. Sketching the Extended Cost Function. 6.6.
Other Important Applications. 6.7. Concluding Remarks. 7. First Steps on
Integral Sums. 7.1. Introduction. 7.2. Integral Sum and Geometric
Interpretation. 7.3. Calculation of Areas. 7.4. Integral Sums. 7.5.
Concluding Remarks. 8. Indefinite Integral. 8.1. Introduction. 8.2.
Indefinite Integral. 8.3. Properties of Indefinite Integral. 8.4. General
Methods of Integration. 8.5. Specific Methods of Integration. 8.6.
Concluding Remarks. 9. Definite Integral. 9.1. Introduction. 9.2.
Properties and Theorems. 9.3. The Fundamental Theorems of Calculus. 9.4.
Applications to the Cost Function. 9.5. Area Calculations. 9.6. Improper
Integrals. 9.7. Concluding Remarks. 10. Series. 10.1. Introduction. 10.2.
Basic Notions about Series. 10.3. Theorems and Applications. 10.4.
Convergence Criteria for Non-Negative Series. 10.5. Non-Positive and
Alternating Series. 10.6. Function Series. 10.7. Power Series. 10.8. Taylor
Series. 10.9. Concluding Remarks.
Real Numbers. 1.3. The Cost Function. 1.4. Function Representation in Table
and Graphic. 1.5. Proofs and Mathematical Reasoning. 1.6. The Inverse
Rationale. 1.7. Discussion of Results. 1.8. Concluding Remarks. 2.
Sequences of Real Numbers. 2.1. Introduction. 2.2. Preliminary Notions.
2.3. Limit and Convergence of a Sequence. 2.4. Theorems About Sequences.
2.5. Study of Important Sequences. 2.6. Notes on Numbers Computation. 2.7.
Concluding Remarks. 3. Limit of a Function. 3.1. Introduction. 3.2. Notions
About Function Limits. 3.3. Lateral Limits at a Point - the Extended Cost
Function. 3.4. Properties of Function Limits. 3.5. Remarkable Limits. 3.6.
Concluding Remarks. 4. Continuity. 4.1. Introduction. 4.2. Continuity at a
Point. 4.3. Continuity on a Range. 4.4. Properties of Continuous Functions.
4.5. Theorems about Continuous Functions. 4.6. Roots of Non-linear
Equations. 4.7. Concluding Remarks. 5. Derivative of a Function. 5.1.
Introduction. 5.2. Derivatives and Geometric Interpretation. 5.3.
Derivation Rules. 5.4. Derivation of Important Functions. 5.5. Derivative
of Inverse Function. 5.6. Derivatives of Different Orders. 5.7. Concluding
Remarks. 6. Sketching Functions and Important Theorems. 6.1. Introduction.
6.2. Important Theorems on Differentiable Functions. 6.3. Maxima and
Minima. 6.4. Asymptotes. 6.5. Sketching the Extended Cost Function. 6.6.
Other Important Applications. 6.7. Concluding Remarks. 7. First Steps on
Integral Sums. 7.1. Introduction. 7.2. Integral Sum and Geometric
Interpretation. 7.3. Calculation of Areas. 7.4. Integral Sums. 7.5.
Concluding Remarks. 8. Indefinite Integral. 8.1. Introduction. 8.2.
Indefinite Integral. 8.3. Properties of Indefinite Integral. 8.4. General
Methods of Integration. 8.5. Specific Methods of Integration. 8.6.
Concluding Remarks. 9. Definite Integral. 9.1. Introduction. 9.2.
Properties and Theorems. 9.3. The Fundamental Theorems of Calculus. 9.4.
Applications to the Cost Function. 9.5. Area Calculations. 9.6. Improper
Integrals. 9.7. Concluding Remarks. 10. Series. 10.1. Introduction. 10.2.
Basic Notions about Series. 10.3. Theorems and Applications. 10.4.
Convergence Criteria for Non-Negative Series. 10.5. Non-Positive and
Alternating Series. 10.6. Function Series. 10.7. Power Series. 10.8. Taylor
Series. 10.9. Concluding Remarks.
1. First Notes on Real Functions. 1.1. Introduction. 1.2. A Function of
Real Numbers. 1.3. The Cost Function. 1.4. Function Representation in Table
and Graphic. 1.5. Proofs and Mathematical Reasoning. 1.6. The Inverse
Rationale. 1.7. Discussion of Results. 1.8. Concluding Remarks. 2.
Sequences of Real Numbers. 2.1. Introduction. 2.2. Preliminary Notions.
2.3. Limit and Convergence of a Sequence. 2.4. Theorems About Sequences.
2.5. Study of Important Sequences. 2.6. Notes on Numbers Computation. 2.7.
Concluding Remarks. 3. Limit of a Function. 3.1. Introduction. 3.2. Notions
About Function Limits. 3.3. Lateral Limits at a Point - the Extended Cost
Function. 3.4. Properties of Function Limits. 3.5. Remarkable Limits. 3.6.
Concluding Remarks. 4. Continuity. 4.1. Introduction. 4.2. Continuity at a
Point. 4.3. Continuity on a Range. 4.4. Properties of Continuous Functions.
4.5. Theorems about Continuous Functions. 4.6. Roots of Non-linear
Equations. 4.7. Concluding Remarks. 5. Derivative of a Function. 5.1.
Introduction. 5.2. Derivatives and Geometric Interpretation. 5.3.
Derivation Rules. 5.4. Derivation of Important Functions. 5.5. Derivative
of Inverse Function. 5.6. Derivatives of Different Orders. 5.7. Concluding
Remarks. 6. Sketching Functions and Important Theorems. 6.1. Introduction.
6.2. Important Theorems on Differentiable Functions. 6.3. Maxima and
Minima. 6.4. Asymptotes. 6.5. Sketching the Extended Cost Function. 6.6.
Other Important Applications. 6.7. Concluding Remarks. 7. First Steps on
Integral Sums. 7.1. Introduction. 7.2. Integral Sum and Geometric
Interpretation. 7.3. Calculation of Areas. 7.4. Integral Sums. 7.5.
Concluding Remarks. 8. Indefinite Integral. 8.1. Introduction. 8.2.
Indefinite Integral. 8.3. Properties of Indefinite Integral. 8.4. General
Methods of Integration. 8.5. Specific Methods of Integration. 8.6.
Concluding Remarks. 9. Definite Integral. 9.1. Introduction. 9.2.
Properties and Theorems. 9.3. The Fundamental Theorems of Calculus. 9.4.
Applications to the Cost Function. 9.5. Area Calculations. 9.6. Improper
Integrals. 9.7. Concluding Remarks. 10. Series. 10.1. Introduction. 10.2.
Basic Notions about Series. 10.3. Theorems and Applications. 10.4.
Convergence Criteria for Non-Negative Series. 10.5. Non-Positive and
Alternating Series. 10.6. Function Series. 10.7. Power Series. 10.8. Taylor
Series. 10.9. Concluding Remarks.
Real Numbers. 1.3. The Cost Function. 1.4. Function Representation in Table
and Graphic. 1.5. Proofs and Mathematical Reasoning. 1.6. The Inverse
Rationale. 1.7. Discussion of Results. 1.8. Concluding Remarks. 2.
Sequences of Real Numbers. 2.1. Introduction. 2.2. Preliminary Notions.
2.3. Limit and Convergence of a Sequence. 2.4. Theorems About Sequences.
2.5. Study of Important Sequences. 2.6. Notes on Numbers Computation. 2.7.
Concluding Remarks. 3. Limit of a Function. 3.1. Introduction. 3.2. Notions
About Function Limits. 3.3. Lateral Limits at a Point - the Extended Cost
Function. 3.4. Properties of Function Limits. 3.5. Remarkable Limits. 3.6.
Concluding Remarks. 4. Continuity. 4.1. Introduction. 4.2. Continuity at a
Point. 4.3. Continuity on a Range. 4.4. Properties of Continuous Functions.
4.5. Theorems about Continuous Functions. 4.6. Roots of Non-linear
Equations. 4.7. Concluding Remarks. 5. Derivative of a Function. 5.1.
Introduction. 5.2. Derivatives and Geometric Interpretation. 5.3.
Derivation Rules. 5.4. Derivation of Important Functions. 5.5. Derivative
of Inverse Function. 5.6. Derivatives of Different Orders. 5.7. Concluding
Remarks. 6. Sketching Functions and Important Theorems. 6.1. Introduction.
6.2. Important Theorems on Differentiable Functions. 6.3. Maxima and
Minima. 6.4. Asymptotes. 6.5. Sketching the Extended Cost Function. 6.6.
Other Important Applications. 6.7. Concluding Remarks. 7. First Steps on
Integral Sums. 7.1. Introduction. 7.2. Integral Sum and Geometric
Interpretation. 7.3. Calculation of Areas. 7.4. Integral Sums. 7.5.
Concluding Remarks. 8. Indefinite Integral. 8.1. Introduction. 8.2.
Indefinite Integral. 8.3. Properties of Indefinite Integral. 8.4. General
Methods of Integration. 8.5. Specific Methods of Integration. 8.6.
Concluding Remarks. 9. Definite Integral. 9.1. Introduction. 9.2.
Properties and Theorems. 9.3. The Fundamental Theorems of Calculus. 9.4.
Applications to the Cost Function. 9.5. Area Calculations. 9.6. Improper
Integrals. 9.7. Concluding Remarks. 10. Series. 10.1. Introduction. 10.2.
Basic Notions about Series. 10.3. Theorems and Applications. 10.4.
Convergence Criteria for Non-Negative Series. 10.5. Non-Positive and
Alternating Series. 10.6. Function Series. 10.7. Power Series. 10.8. Taylor
Series. 10.9. Concluding Remarks.