Mathematics for Management -- Supplementary Electronic Materials

Welcome to the Supplementary Electronic Materials
for Mathematics for Management

 

Calculus II for Management

Calculus II -- Structure
 
 
Dear students,
 
let us welcome you to the course "Calculus II" where we will continue our breath-taking adventures in university mathematics by covering topics of linear algebra (introduction to vectors and matrices) and multi-variable differential and integral calculus. I.e. based on the knowledge and skills gathered during Calculus I, we now etxend these to every-day settings in Economics and lay the foundations that con can deal sucessfully with hundereds and thousands of items entering functions in real business and management challenges.
 
These supplementary electronic materials are intended to help you beyond the lectures and tutorials especially such that you can revisit certain topics and have them explained in a short video clip of about 15-20 minutes and, for each small unit, take a knowledge quizz to test your learning progress.
 
Moreover, a "learning path" guides you through the materials such that you always know which parts are based on which and thus to systematically track the foundations of the topics. This may especially be helpful in case you missed some lectures so that you can easily find yourself again in the course structure.
 
Note, the supplementary electronic materials are structured topic-wise. Though, during the lecture, we will choose a more learning centeres approach and extend the discussion of the linear algebra part over the complete semester so that there is a continuous rehearsal and not just a five weeks block at the start of the term.
 

Please, select one of the following parts

To proceed with using the supplementary electronic materials, please, choose one of the following parts and get to the corresponding learning path for the constituting sections:
 
  • Introduction to Vectors & Matrices (4 sections)
    • Linear Systems of Equations
    • Determinants
    • Linear Combinations of Vectors
    • Matrix Computations
  • Advanced Topics in Integration (4 sections)
  • Functions in Several Variables & Optimization (4 sections)
  • Double & Nested Integrals (2 sections)

Our course structure per semester week

The following table connects the parts and sections of the supplementary electronic materials with the course structure per semester incl. the slides of the lectures and homework assignement. Please, note the homework assignments here may vary from the actual ones given in your course. Though, you can always use them as additional material to prepare for quizes.
 
WeekTopicSlidesHomework
Part: Introduction to Vectors & Matrices
1

Linear Systems of Equations:

  • Lines in the plane & 2D systems of equations (e-material)
  • Planes in space & 3D systems of equations (e-material)
 slides [.pptx] homework
2

Determinants:

  • N-Variable systems of equations & Gaussian Elimination (e-material)
  • Motivation: the geometry of determinants (e-material)
 slides [.pptx] homework
3

Determinants II & Linear Combinations of Vectors:

  • General properties & computation rules (e-material)
  • Vectors & their linear combinations (e-material)
 slides [.pptx] homework
4

Vector & Matrix Computations:

  • Scalar-product, vector-product & spat-product (e-material)
  • Matrix-matrix multiplication (e-material)
 slides [.pptx] homework
Part: Advanced Topics in Integration
5

Introduction to Ordinary Differential Equations (ODEs):

  • Ordinary Differential Equations (e-material)
  • Separable ODEs (e-material)
  • Continuous compounding (e-material)
  • Linear ODEs (e-material)
  • Diffusion of innovation, epidemics, and rumor (e-material)
 slides [.pptx] homework
6

Improper Integrals:

  • A primer on eigenvalues and eigenvectors (e-material)
  • The improper integral (e-material)
  • Application of improper integrals (e-material)
  • Survival & renewal in perpetuity (e-material)
  • Population of an urban area (e-material)
 slides [.pptx] homework
7

Numeric Integration & Linear ODEs:

  • Approximation by rectangles (e-material)
  • Approximation by trapezoids (e-material)
  • Approximation by using Simpson's Rule (e-material)
  • Interpreting data with numerical integration (e-material)
  • A Primer on Inverse Matrices (e-material)
 slides [.pptx] homework
8

Introduction to Continuous Probability:

  • Continuous random variables & probability density functions (e-material)
  • Examples of uniform, exponential, and normal probability density functions (e-material)
 slides [.pptx] homework
Part: Curve Sketching & Optimization
9

Functions in Several Variables:

  • Vector algebra revisited: the Hessian Normal Form (e-material)
  • Functions in several variables & their applications (e-material)
  • Graphs of functions of two variables (e-material)
  • Level curves & their use in economics (e-material)
  • Partial derivatives (e-material)
 slides [.pptx] homework
10

Partial Derivatives & Optimizing Functions of Two Variables:

  • Partial derivatives in economics (e-material)
  • The Chain Rule (e-material)
  • Optimizing functions of two variables (e-material)
  • The Second Partials Test (e-material)
 slides [.pptx] homework
11

Optimization & The Method of Least Squares:

  • Finding extreme values on a closed and bounded region (e-material)
  • Matrix algebra revisited
  • The least-squares procedure & line (e-material)
  • Least-squares prediction (e-material)
  • Nonlinear curve-fitting (e-material)
 slides [.pptx] homework
12

Constrained Optimization: The Method of Lagrange Multipliers:

  • Intro & applications in economics (e-material)
  • The significance of the Lagrange multiplier (e-material)
  • Why the method of Lagrange multipliers works (e-material)
  • Application in 3D (e-material)
 slides [.pptx] homework
Part: Integration & Wrap-up
13

Double Integrals:

  • Double integrals over a rectangular region (e-material)
  • Double integrals over non-rectangular regions (e-material)
  • Applications (e-material)
 slides [.pptx] homework
14

Applications of Double Integrals:

  • Further examples of double integrals (e-material)
  • Properties of double integrals (e-material)
  • Double integrals in probability
 slides [.pptx] homework
15

Recap of the Course & Preparation for the Final Exam:

  • Essential theorems and connections between concepts
  • Examples
 slides [.pptx]
 
 

Literature

  • L. Hoffmann, G. Bradley, D. Sobecki, and M. Price (2013): Calculus for Business, and the Social and Life Sciences, 11th edition, Mc Graw Hill [main course text book]
  • F. Aleskerov, H. Ersel, and D. Piontkovski (2011): Linear Algebra for Economists, Springer [additional reading]
  • M.L. Bittinger, D.J. Ellenbogen, and S.A. Surgent (2012): Calculus and its Applications, Addison-Wesley [additional reading]
  • S. Stewart (2016): Calculus - Early Transcendentals, 8th edition, Cengange [additional reading]
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