## Natural Science

**PHY 101 Physics I: Mechanics and Thermodynamics**

Topics include: Units and physical quantities, vectors, motion in 1-dimension, motion in more than 1-dimension, Newton’s laws of motion and their applications, work and energy, potential energy and conservation law of energy, momentum and impulse, rotation of rigid bodies, dynamics of rigid bodies, gravitation, thermal properties of matter, laws of thermodynamics.

Pre-requisite: None

**PHY 101L Mechanics and Thermodynamics Lab**

Experiments include: simple harmonic motion observed through webcam, waves and oscillations, standing waves, resonance, moment of inertia of a tennis ball, rotational mechanics, rotational inertia, rotational friction, conservation of energy, latent heat of liquid nitrogen, heat capacity of solids, determined from boil-off of liquid nitrogen, conservation of momentum – elastic and inelastic collision, rotational motion, mass on a spring, basics of uncertainty analysis, Maxwell’s wheel, light polarization, heat transfer, conduction, convection, Newton’s law of cooling, temperature oscillations, Fourier analysis.

Pre-requisite: PHY 101

**PHY 102 Physics II: Electricity & Magnetism**

Topics include: Electromagnetism and electrostatics, electric charge, Coulomb’s law, electric field, Gauss’s law, electrostatic potential, magnetic fields, Biot-Savart law and Ampere’s law, magnetic materials, time-varying fields and Faraday’s law of induction, Hall effect, displacement current and Maxwell’s equations.

Prerequisite: PHY 101

**PHY 102L Advanced Physics Lab**

Experiments include: determination of Curie point of a Ferro-magnet by controlled electric heating, observing Hall effect in semiconductors, magnetic moment of a conductor loop in a magnetic field, determining Verdet’s constant, Frank-Hertz Meter, determination of Planck’s constant from the spectrum of a tungsten light bulb, optical activity of a chiral (sugar) solution, imaging electron trajectories using a magic eye, image analysis, Lenz’s Law, band gap measurement of pure Ge, magnetic pendulum, exploring phase portraits, chaos, bifurcations, Spectral Lines of different gasses.

Pre-requisite: PHY 102

**PHY 201 Modern Physics**

Topics include: Review of basic mechanics, introduction to special relativity, relativity and Physics, Planck’s radiation law, photo electric effect, Compton scattering, pair production, Bohr’s theory of Hydrogen atom, basics in quantum mechanics, Schrodinger’s equation and its applications, ideal gas equation, Maxwell’s distributions, Boltzmann’s distributions, Identical particles

Pre-requisite: PHY 101, PHY 102, MATH 102, MATH 201/203

**PHY 202 Quantum Mechanics**

Topics include: Particle aspects of radiation, wave aspects of particles, quantum systems and indeterminacy, quantization rules, wave packets, mathematical tools of quantum mechanics, postulates of quantum mechanics, one-dimensional problems in quantum mechanics, angular momentum, more than 1-dimensional problems, rotations and addition of angular momenta, time dependent and independent approximation methods in quantum mechanics, scattering theory.

Pre-requisite: PHY 101, PHY 201, MATH 201/203

**PHY 301 Classical Mechanics**

Topics covered: Survey of elementary particles, variational principles and Lagrange’s equations, central force problem, kinematics of rigid body motion, the rigid body equations of motion, oscillations, the Hamilton’s equations of motion, canonical transformations, continuous classical systems.

Pre-requisite: PHY 101, MATH 201/203

**PHY 302 Mathematical Methods for Physics **

Topics include: Tensors and their role in Physics, complex variable theory, linear integral equations, green’s functions, introduction to group theory.

Pre-requisite: MATH 201/203

**PHY 401 Quantum Mechanics II**

Topics include: Recapitulation of classical field theory, path integrals in quantum mechanics, relativistic scattering theory, Quantum Mechanics and relativity, Klein Gordon equation, Dirac equation and representations of its solutions, (discrete) symmetries, basic understanding of interactions in quantum field theory.

Pre-requisite: PHY 202, PHY 301, PHY 302

**BIO 101 Cell Biology & Public Health**

This course provides an introduction to cellular and molecular biology and builds its connection with human biological processes; there will be a prime focus on developing skills to communicate biological concepts to laymen. Topics include: Prokaryotic and eukaryotic cells, structure and function of cellular organelles, cells tissues and organ systems, movement across cell membranes, cellular reproduction, DNA replication, transcription and translation, Mendelian genetics, blood groups, introduction to the immune system and vaccines, dengue viral infection, and cancer development. Workshop on communication design in public health will be integrated.

Pre-requisite: None

**BTEC 101 Introduction to Biotechnology**

This course provides an introduction to the fundamentals of biotechnology and its applications. Topics include: overview of biotechnology and its current importance in society, rapid growth of biotechnology in agriculture, environment, industry and medicines, antibiotics/antibodies biotech. Emphasis will be placed on DNA manipulation sciences including genetic engineering, gene cloning, plasmids as cloning vectors, restriction enzymes, DNA ligase, PCR, biotransformation, E. coli host as model system, mutagenesis, manipulation of expression of desired DNA, strategies of protein purification, stem cell biotech and ethics of biotechnology.

Prerequisite: School / college level Biology or chemistry or permission of instructor.

**BTEC 101L Biotech Laboratory Practices **

This laboratory course provides practical insights into the role of DNA sciences in achieving and improving the technological applications to develop products to improve quality of life. Topics include: basic operations used in biotech lab, DNA extraction from living organisms, DNA cut and clone, making lots of copies of DNA, overproduction of protein, purification, plasmid isolation, DNA manipulation by PCR, transformation of E. coli with a recombinant plasmid, DNA purification and quantification, calorimetric detection of DNA, visualizing of DNA on gel electrophoresis and DNA fingerprinting.

Co-requisite: BTEC 101

**ENVS 100 Climate Change and Us**

This course will develop a conceptual understanding of various issues and impacts related to climate change and provide an opportunity to innovate and implement sustainable solutions. Throughout the course students will see climate change from the lens of history, capitalism, water, cities, food, ocean, glaciers, forests, conflicts and policies. Students will study the Global Action Plans on climate change including the Paris Agreement.

Pre-requisite: None

**SCI 100 Introduction to Sustainability **

This course is designed to introduce the essential concepts of sustainability. This subject is of vital importance as it seeks to uncover the principles of the long-term survival and welfare of all the inhabitants of our planet. The course is intended to be useful for both a broad-based introductory class on sustainability and as a useful supplement to specialist courses which wish to review the sustainability dimensions of their areas of study. By covering a wide range of topics, review questions, case studies, and links to further resources, students will become conversant in the language and concepts of sustainability and will be equipped for further study in sustainable management, planning, policy, economics, climate, ecology, infrastructure, and more.

Pre-requisite: None

### Mathematics

**MATH 012 Pre-Calculus**

Topics include: a revision of the number systems and relations, functions and polynomials with symbolic and graphic representations. These topics will cover a wide range of subtopics to bridge the gaps in high school mathematics, like rational functions, inverse functions, logarithmic and exponential Functions followed by trigonometric Functions with an extensive treatment in the course. As a learning outcome students are expected to be able to analyze functions and their behaviors symbolically, numerically and graphically.

Pre-requisites: High school mathematics of any level.

**MATH 101 Calculus I**

Topics include: an overview of functions and their behavior in terms of rates of change, average vs. instantaneous rates of change, the derivative and shortcuts to differentiation, optimization (finding relative extrema / critical points), related rates, area under a curve, Riemann sums and the definite integral, the general antiderivative, approximation of definite integrals, techniques of integration and improper integrals.

Prerequisites: None

**MATH 102 Calculus II**

Topics include: a look at finding volumes of revolution using a Riemann Sums approach to integration, an introduction to first order differential equations and slope fields, parametric equations and graphs and finding area and arc length of parametric curves, polar coordinates and polar functions with areas and arc length of polar curves, functions of severable variables, partial derivatives and the equation of a tangent plane to a surface, basic vector algebra with dot and cross product derivations, directional derivatives, optimization and the second derivative test for functions of two variables, optimization with Lagrange multipliers, integrating functions of several variables with double and triple integrals evaluated in Cartesian, cylindrical and spherical coordinates, parametrization of lines and curves in 3-space, vector fields, line integrals and the fundamental theorem of calculus for line integrals.

Prerequisites: MATH 101

**MATH 105 The Art of Mathematics**

This course will explore multiple theorems, arguments and quantities that have been relevant to a variety of fields through history, such as art, architecture, astronomy, and the physical sciences. Tracing the birth of geometric reasoning from the time of Euclid to looking at the birth of trigonometry as a tool for astronomical calculations and models, students will be introduced to geometry, algebra, and topology through various contexts. Students will be expected to use these concepts to create culminating projects using design and mathematical software.

Note: This course will also fulfil one of the math requirements for the students pursuing a Communication and Design major.

Prerequisites: None

**MATH 106 Music and Mathematics**

This course will introduce the rudiments of Western and South Asian musical theory, with a focus on the mathematics incorporated in their development and overall structure. The course will explore the properties of the twelve-tone scale, the historical evolution of tuning and temperament, the idea of combinational tones and consonance, and the physics behind the construction of musical instruments. Looking primarily at South Asian and Western musical genres, students will also analyze the mathematics involved in music composition, for both melody and rhythm.

Prerequisites: None

**MATH 202 Engineering Mathematics**

Topics include: Vector Calculus (vector functions, line and surface integrals). Elementary methods for solving first order ODEs (direct integration and substitution) with geometric interpretation and classification, separable ODEs, method of integrating factors. Vector algebra (including matrix algebra, eigenvalues and eigenvectors, quadric surfaces). Dynamical systems (linear systems of ODEs, stability and phase portraits of dynamical systems). Second order ODEs – elementary methods including their classification, reduction of order techniques, linear second order ODEs with constant coefficients, finding particular solutions. Orthogonal functions and Fourier series solutions (generalized and trigonometric methods), convergence in the mean and pointwise convergence, odd and even expansions, half-range expansions. Partial differential equations (PDEs) (wave, heat and Laplace equations), solutions using Fourier series and Laplace transforms. Schrӧdinger equation.

Prerequisite: MATH 102

**MATH 203 Advanced Differential Equations**

Topics include: A brief revision of first- and second-order ordinary differential equations (ODEs) with constant coefficients. Differential operators, Wronskian and linear independence. Numerical solution methods for ODEs: Euler method, Taylor series solution up to 2nd order, Runge-Kutta methods up to 2nd order. Cauchy-Euler equations. Power series and Frobenius’ methods including Ordinary points, singular points, regular points, analytic functions, indicial equation. Bessel function and Bessel’s equation, Legendre equations. Boundary value problems for homogeneous linear 2nd order ODEs: Boundary values, Sturm-Liouville problem, Eigen functions and corresponding eigenvalues, Fourier Bessel series, inner products and norms of functions, Self-adjoint operators, and the Schrӧdinger equation.

Prerequisites: MATH 201 for CS and EE students. MATH 102 with min 70% score for non-engineering students in MATH Minor.

**MATH 205 Linear Algebra**

Topics covered: a brief revision of vector algebra including lines and planes in 3D and matrices, determinants, symmetric matrices and quadratic forms, elementary row and column operations of a matrix, systems of linear equations and their solutions, existence and uniqueness of solutions, vector spaces, inner products and ortho-normalisation, as well as orthogonal transformations and rotations, linear transformations, orthogonality, QR factorization, Hermitian and Unitary transformations, least squares analysis and approximations, singular value decomposition, direct sum decomposition and the Caley-Hamilton Theorem.

Prerequisite: MATH 201

**MATH 401 The Time Scale Calculus**

Topics covered: the discrete and continuous unified – motivation, elementary definitions, continuity on time scales, the Delta-differentiation, the Delta-integration, linear theory of time scales – the tools to model stop-start processes (the time scale exponential, logarithmic functions on time scales, trigonometric and inverse trigonometric functions on time scales), and introduction to dynamic equations on time scales (first- and second-order).

Prerequisite: MATH 102