Calculus 1 (for IEM)

Uitgebreide vaknaam	Calculus 1 (for IEM)
Leerdoelen	After completing this course students should be able to: 1. calculate limits using the limit laws, the Squeeze Theorem and l'Hospital's rule. 2. calculate derivatives by applying the product rule, quotient rule, and chain rule, and combinations thereof. In addition, the student can use these techniques to find the local and absolute extreme values of a given function. 3. calculate Taylor expansions of concrete functions and use these expansions to compute limits and approximations for definite integrals. 4. calculate integrals using the standard techniques of integration (substitution rule, integration by parts, trigonometric integrals and substitutions, integration of rational functions by partial fractions) and is able to recognize which technique is best used in a given situation. 5. calculate with complex numbers, can plot them in the complex plane, is able to formulate and use DeMoivre's Theorem, can compute roots of a complex number and can solve equations in that way. The student can state the definition of the complex exponential function and can use that in applications. 6. solve separable first-order differential equations and can calculate the general solution of a first-order linear differential equation by means of an integrating factor. 7. solve homogeneous second-order differential equations with constant coefficients and calculate a particular solution for nonhomogeneous equations using the method of undetermined coefficients.
Omschrijving	The course starts with refreshing and improving the basic mathematical skills (BMS). In the fourth week of the course a diagnostic test is taken: students who score less than 7 out of 10 points are asked to do extra exercises using the electronic learning environment SOWISO. Then real functions of one real variable are treated: standard and composed functions, models, limits, derivatives, extreme values, Taylor expansions, and integrals (applications and techniques). Subsequently complex numbers are introduced, an imaginary extension of the real numbers. Finally, differential equations are solved to describe processes in physics, economy, medical sciences, etc. This topic includes: initial value problems, directional fields, equilibrium solutions and stability, separation of variables, variation of constants, homogeneous and inhomogeneous equations, and conversion of complex solutions into real-valued solutions. The material is illustrated through examples that focus on the applications of mathematical techniques.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Werkcollege (T) (Total hours of lectures: 24 hours, tutorials: 24 hours, self-study: 92 hours)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT) (C = (80%Written exam+20%BMS test)/10 is the combined grade for the exam and the BMS test If C < 5.5, then the final grade is G = C, students must pass the final with a score of 4.5 or higher. If C >= 5.5, then the final grade is G = max(C, 0.7*C + 0.2*Interim test + 0.1*Homework assignments) The student passes for the course unit if G >= 6.)
Vaksoort	propedeuse
Coördinator	A.M.S. Waters, PhD.
Docent(en)	dr. ir. R. Luppes , A.M.S. Waters, PhD.
Verplichte literatuur	Titel Auteur ISBN Prijs Calculus. Early transcendentals. Newest (8th) Edition (International Metric Edition). Cengage Learning James Stewart 978-1-305-27237-8 The reader “Basic Mathematical Skills” is made freely available on Nestor
Entreevoorwaarden	The course unit assumes only prior knowledge acquired from Mathematics B as taught in pre-university programmes (VWO) on Dutch secondary schools (or equivalent).
Opmerkingen	The course unit is followed by, and prepares students for, the course units Linear Algebra and Calculus 2 in which the learning objectives attained are recommended as prior knowledge.
Opgenomen in	Opleiding Jaar Periode Type BSc Industrial Engineering and Management 1 semester I a verplicht