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## ENGG2012B Lecture 1

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**ENGG2012BLecture 1**Kenneth Shum ENGG2012B**Lecturer**• SHUM W. K. Kenneth(沈穎祺) • Office: SHB 736 • inside Institute of Network Coding • Email: wkshum @ … • Web: kshum.com • Office hour: T, W 2:00~3:00, or by appointment ENGG2012B**Tutors**• LONG Feichi (龍非池) • Office: SHB 729 • Email: lf012 @ … • YU Haoran (余皓然) • Office: SHB 825 • Email: yh012 @ … 729 is a power of 3 729 = 333333 ENGG2012B**Web**• Course webpage https://course.ie.cuhk.edu.hk/~engg2012b/ • E-learning platform https://elearn.cuhk.edu.hk • Announcements, discussions etc. ENGG2012B**Syllabus**• Complex Variables • complex number, analytic functions, complexfunctions, power series and convergence tests • Linear Algebra • matrices, systems of linear equations and solutions, determinants, rank, eigenvalues and eigenvectors • Numerical Methods • Numerical integration and differentiation, numerical methods in linear algebra • Probability and statistics ENGG2012B**Learning Outcome**• Manipulate complex numbers and complex functions comfortably • Express a function as a power series • Be familiar with a variety of convergence tests • Determine the type of a matrix (e.g. orthogonal, unitary, Hermitian …) • Solve equations using matrices. • Calculate basic probabilities and statistics ENGG2012B**Grading**• Biweekly homework, 12% • Midterm test, 38% • Final exam, 50% ENGG2012B**Academic Honesty**• Attention is drawn to University policy and regulations on honesty in academic work, and to the disciplinary guidelines and procedures applicable to breaches of such policy and regulations. Details may be found at http://www.cuhk.edu.hk/policy/academichonesty/ ENGG2012B**Reference texts**“Advanced Engineering Mathematics” by Ervin Kreyszig, 10th edition, John Wiley & Sons. “Advanced Engineering Mathematics” by Michael Greenberg, 2nd edition, Prentice Hall. Erwin O. Kreyszig (6/1/1922~12/12/2008) ENGG2012B**Course outline**• Before midterm (no calculus, more algebraic) • Linear algebra, vector, matrix • Numerical methods for linear algebra • Discrete probability • Complex variables and functions • After midterm (with calculus, more analytic) • Power series • Numerical methods for integration • Continuous probability • Complex differentiation and integration ENGG2012B**Roadmap**ENGG2012B**System of two equations**Two variables, two equations ENGG2012B**System of three equations**Three variables, three equations ENGG2012B**System of Linear Equations**Multiple variables, multiple equations How to solve it? ENGG2012B**Determinant**• Area of parallelogram (c,d) (a,b) ENGG2012B**3x3 Determinant**• Volume of parallelepiped (g,h,i) (d,e,f) (a,b,c) ENGG2012B**Nutrition problem**• Find a combination of food A, B, C and D in order to satisfy the nutrition requirement exactly. How to solve it using linear algebra? ENGG2012B**Electronic Circuit (static)**• Find the current through each resistor System of linear equations ENGG2012B**Electronic Circuit (dynamic)**• Find the current through each resistor This is a topic in ENGG2011 alternatingcurrent inductor System of differential equations ENGG2012B**Electronic Circuit (stochastic)**• How about randomness and thermal noise? This is a topic in ELEG3410 thermal noise alternatingcurrent Inductance variesaccording to voice ENGG2012B**Probability**• What is the chance of winning the first prize of mark six? • Binomial coefficient • The total number of ways that we can pick k out of n distinct object = • Notations: • (pronounced as “n choose k”) http://www.youtube.com/watch?v=ETFOTboBMHE ENGG2012B**Expected gain**• Probability of first prize • Suppose that the first prize is $100,000,000, and you have $10. Decision Not buy buy Expected value $7.15 $10 ENGG2012B**Complex numbers**• Useful in solving polynomials Im Complexplane Re ENGG2012B**Roots of unity**Complex plane Im -1 Re 1 ENGG2012B