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E-raamat: Calculus for Engineering Students: Fundamentals, Real Problems, and Computers

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Edited by , Edited by (University of Salamanca, Spain), Edited by (Department of Multidisciplinary Technologies, College of Engineering and Built Environment Technological University Dublin, Ireland), Edited by (Department of Applied Mathematics, School of Industrial Engineerin)
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Calculus for Engineering Students: Fundamentals, Real Problems, and Computers insists that mathematics cannot be separated from chemistry, mechanics, electricity, electronics, automation, and other disciplines. It emphasizes interdisciplinary problems as a way to show the importance of calculus in engineering tasks and problems. While concentrating on actual problems instead of theory, the book uses Computer Algebra Systems (CAS) to help students incorporate lessons into their own studies. Assuming a working familiarity with calculus concepts, the book provides a hands-on opportunity for students to increase their calculus and mathematics skills while also learning about engineering applications.

  • Organized around project-based rather than traditional homework-based learning
  • Reviews basic mathematics and theory while also introducing applications
  • Employs uniform chapter sections that encourage the comparison and contrast of different areas of engineering
About the editors xiii
Preface xv
1 Limits and apparent paradoxes in economics and engineering
1(14)
Victor Gayoso Martinez
Luis Hernandez Encinas
Agustin Martin Munoz
1.1 Limit of a function
1(7)
1.2 Areas of application
8(1)
1.3 Challenging problems
8(5)
1.4 Conclusions
13(1)
References
14(1)
2 Derivative: tool for approximation and investigation
15(24)
Petr Habala
2.1 Derivative: overview of theory
15(4)
2.2 Derivative in applications
19(1)
2.3 Exploring derivative
20(17)
References
37(2)
3 Complex numbers and some applications
39(22)
Fatih Yilmaz
3.1 Introduction
39(12)
3.2 Illustrations
51(2)
3.3 Quaternions
53(7)
References
60(1)
4 Sequences and series: a tool for approximation
61(24)
Petr Habala
4.1 Sequences and series: overview of theory
61(6)
4.2 Sequences and series in applications
67(1)
4.3 Exploring sequences and series
68(15)
References
83(2)
5 Vibrations and harmonic analysis
85(34)
Daniela Richtarikova
Milos Musil
5.1 Basic theory background
85(9)
5.2 Fourier series in applications
94(7)
5.3 Mechanical vibration forced by periodic force with viscous damping: harmonic analysis of a force, stabilized output movement obtained by principle of superposition
101(16)
References
117(2)
6 Applications of integral calculus
119(18)
Ion Mierlus-Mazilu
Stefania Constantinescu
Lucian Nita
Cesar de Santos-Berbel
6.1 Key ideas on the calculus of primitive integrals
119(3)
6.2 Description of general problems and areas where they are very common
122(3)
6.3 Challenging problems
125(9)
References
134(3)
7 Multiple integrals in mechanical engineering
137(20)
Deolinda M.L. Dias Rasteiro
Manuel Rodriguez-Martin
Pablo Rodriguez-Gonzalvez
7.1 Background
137(10)
7.2 Applications of multiple integrals
147(3)
7.3 Real problems
150(6)
References
156(1)
8 Critical forces and collisions. How to solve nonlinear equations and their systems
157(22)
Monika Kovacova
Daniela Richtarikova
8.1 Preliminaries
157(7)
8.2 Why the nonlinear systems of equations are important. How important it is to study nonlinear systems
164(1)
8.3 Nonlinear equations and their systems in applications
165(13)
References
178(1)
9 Shortest path problem and computer algorithms
179(18)
Deolinda M.L. Dias Rasteiro
9.1 Background
179(5)
9.2 Description of general path problems and areas where they are very common
184(2)
9.3 Real problems
186(5)
9.4 Combined network problems
191(4)
References
195(2)
10 Random variables as arc parameters when solving shortest path problems
197(24)
Deolinda M.L. Dias Rasteiro
Nelson Chibeles-Martins
10.1 Background
197(2)
10.2 Description of general problems and areas where they are very common
199(10)
10.3 Real problems
209(9)
References
218(3)
11 Snails, snakes, and first-order ordinary differential equations
221(24)
Alberto Alonso Izquierdo
Ascension H. Encinas
Miguel Angel Gonzalez Leon
Angel Martin del Rey
Jesus Martin-Vaquero
Araceli Queiruga-Dios
Gerardo Rodriguez
11.1 Background
221(6)
11.2 Description of general problems and areas where they are very common
227(5)
11.3 Real problems
232(10)
References
242(3)
12 Oscillations in higher-order differential equations and systems of differential equations
245(28)
Lucian Nita
Ion Mierlus-Mazilu
Leonard Daus
Daniela Richtarikova
Manuel Rodriguez-Martin
Pablo Rodriguez-Gonzalvez
12.1 Basic theory background
245(11)
12.2 Higher-order differential equations in practice
256(3)
12.3 Challenging problems in applications
259(12)
References
271(2)
13 Partial differential equations
273(32)
Cormac Breen
Michael Carr
13.1 Introduction
273(5)
13.2 Applications of partial differential equations
278(9)
13.3 Real engineering problems
287(18)
14 Laplace transforms
305(22)
Michael Carr
Mark McGrath
Eabhnat Ni Fhloinn
14.1 Introduction to Laplace transforms
305(10)
14.2 Solving first-and second-order differential equations
315(3)
14.3 Engineering applications of Laplace transforms: problems
318(9)
15 Specific mathematical software to solve some problems
327(22)
Alberto Alonso Izquierdo
Miguel Angel Gonzalez Leon
Jesus Martin-Vaquero
Deolinda M.L. Dias Rasteiro
Monika Kovacova
Daniela Richtarikova
Pablo Rodriguez-Gonzalvez
Manuel Rodriguez-Martin
Araceli Queiruga-Dios
15.1 Vibration and harmonic analysis
327(7)
15.2 Critical forces - how to solve nonlinear equations and their systems
334(1)
15.3 Shortest path problem and computer algorithms
335(7)
15.4 Snails, snakes, and first-order ordinary differential equations
342(3)
15.5 Oscillations in higher-order differential equations and systems of differential equations
345(2)
References
347(2)
Index 349
Jesús Martín Vaquero is an Associate Professor at the Department of Applied Mathematics, University of Salamanca. He belongs to the Research Group in Cryptography, Information Security and Discrete Mathematics (GICSIMAD), which since 2007 a Recognized Research Group (GIR) of the University of Salamanca. Throughout this time he has participated in national and regional R + D + I projects. His research has been published in the SIAM Journal on Scientific Computing, Journal of Computational and Applied Mathematics, International Journal of Modern Physics, Journal of Computational and Applied Mathematics. Micahel Carr has worked in the development of core mathematical skills, mathematics education for engineers, and mathematical education in Irish prisons. He has published innthe European Journal of Engineering, the Proceedings of the 45th SEFI Annual Conference, and the 41st SEFI conference. Araceli Queiruga Dios is a lecturer in Mathematics at the Department of Applied Mathematics at the School of Industrial Engineering in Béjar, Spain. She studies public key cryptography as well as educational tools and mathematical applications for engineering students. She has published in the International Journal of Computer Mathematics and in the Lecture Notes in Computer Science (bioinformatics and artificial intelligence). Daniela Richtáriková has teached mathematics and related subjects at Slovak University of Technology in Bratislava since 1992. She finished her studies at Comenius University, and received her PhD at Slovak University of Technology. Her main research interests include fractal geometry, elements of chaos theory, and relationships between mathematics and art. Nowadays, she focuses on applied mathematics and pedagogical research in the field of active and competency based mathematical education. She is the author of more than 80 papers and two textbooks. She acts as an executive secretary in the Slovak Society for Geometry and Graphics, the editor of the scientific journal G Slovak journal for Geometry and Graphics”, and as the organizer of international conferences. She has cooperated in a number of national and international educational and research projects.
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