# Course Descriptions

**PHYSICS ***(1 high school credit/year)*

CVGS physics is a college level introduction using basic calculus and vector analysis to study the particle and wave nature of everyday phenomena. Topics include Newtonian and fluid mechanics, conservation laws, thermodynamics, vibrations and waves, electricity and magnetism, optics, and modern physics. Concepts are explored and applied through hands-on activities and in a computer-based laboratory through investigations requiring data collection and analysis or use of models and computer simulations that show interdisciplinary relationships between physics, life sciences, mathematics, and technology. Development of problem solving, analytical thinking, laboratory, and communication skills is also stressed.

**MATH ANALYSIS ***(1 high school credit/year & 7 college credits through CVCC: MTH 166 and MTH 168)*

Math Analysis is a pre-calculus course that includes an in-depth conceptual analysis of algebraic, polynomial, rational, logarithmic, exponential, and trigonometric functions. Topics include graphical behavior, domains and ranges, roots (real & complex), the first derivative, graphing, application problem solving and data analysis, and an introduction to integration. Parametric equations are presented with a focus on applications and conceptual analysis. Analysis includes required algebraic proofs and/or conceptual explanations in written and oral presentations. Graphing calculators, spreadsheets, and a computer algebra system are used extensively. The study of matrices is included, and optional topics include an introduction to sequences and series.

**JUNIOR RESEARCH ***(1 high school credit/year)*

This unique course is an introduction to the research process including literature research, project design, elementary statistical analysis, scientific writing and multimedia presentations. Each student completes an individual research project. Students design a study, collect and analyze data, and report the results in paper, PowerPoint, poster and webpage formats. The statistical analysis of data is conducted using MicroSoft Excel. During the second semester students complete a 36-hour internship. Additional information about the junior year internship experience can be found on our website at http://www.cvgs.k12.va.us/academics/internships.

**CALCULUS OF A SINGLE VARIABLE*** (1 high school credit/year and 4 college semester credits per semester: CVCC courses MTH 173, MTH 174)*

These courses comprise a college level study of differential and integral calculus. Topics include the study of limits, continuity, derivatives (definition, concepts), differentiation techniques (including inverse trigonometric functions and polar and parametric curves), curve sketching, optimization applications, antiderivatives, definite and indefinite integrals, Fundamental Theorems of Calculus, integration techniques, improper integrals, Trapezoidal and Simpson’s Rules, applications of the definite integral including geometry, density, center of mass and work, Infinite Series including Taylor Polynomials, separable differential equations with applications, slope fields, and Euler’s Method. Upon successful completion of each semester course, students earn 4 semester credits from CVCC.

**COMPUTER SCIENCE** *(1 high school credit/year and 4 college semester credits per semester: CVCC courses CS 201 and CS 202)*

This college level sequence introduces algorithm and problem solving methods and emphasizes structured programming concepts. Students examine constructs for logic control, sequencing statements, input/output, searching and sorting and explore data structures including lists, trees, queues and stacks. This sequence also teaches object oriented programming techniques by making use of methods, classes and objects to demonstrate the object oriented concepts of encapsulation, inheritance, and polymorphism. Upon successful completion of each semester course, students earn 4 semester credits from CVCC.

**HUMAN ANATOMY & PHYSIOLOGY** *(1 high school credit/year and 4 college semester credits per semester: CVCC courses BIO 141 and BIO 142)*

This college level sequence provides an overview of cellular physiology and reviews many human organ systems including the nervous, respiratory, circulatory, digestive, skeletal, endocrine, muscular, urinary, reproductive, and lymphatic systems. Students explore organ systems through the use of interactive modeling and discuss current medical cases with local health care professionals. Upon successful completion of each semester course, students earn 4 semester credits from CVCC.

**CONNECTIONS IN MATHEMATICS** *(1 high school credit/year)*

This course provides students with introductory experiences in symbolic logic, graph theory, probability, voting schemes and apportionment methods, personal finance, mathematical proofs, differential and integral calculus, and separable differential equations. Emphasis is placed on conceptual understanding, solving real world applications, using technology, and fostering mathematical reasoning and communication.

**LINEAR ALGEBRA/VECTOR CALCULUS*** (1 high school credit/year and 7 college semester credits/year: CVCC courses MTH 285 and MTH 277)*

This sequence is a college level study of linear algebra and vector calculus. Linear algebra includes systems of equations, matrices, vector spaces, linear transformations, bases, dimension, eigenvalues, eigenvectors, and orthogonality. Vector calculus includes vector-valued functions, functions of several variables, vector fields, partial derivatives and multiple integrals. Both semesters emphasize computational techniques, geometry and theoretical structure, creative problem solving, and proofs. Upon successful completion of Linear Algebra, students earn 3 semester credits, and successful completion of Vector Calculus awards 4 semester credits from CVCC.

**SENIOR SEMINAR*** (1 high school credit/year)*

During the first six-weeks period students participate in an engineering design-build-test project with local engineers serving as mentors. For the remaining five six-weeks periods students explore and use sophisticated technologies choosing from among biotechnology, desktop publishing, electron microscopy, 3D design and printing, scientific photography, microbiology, nuclear science, robotics, video production, Photoshop, and iPad application design.