Math 55b pdf

As of March 16,current online class instruction continues as scheduled. District and College campuses are closed until further notice. For labs or limited in-person classes that have yet to be converted online, they are suspended and your faculty will contact you with further information.

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Visit The Online College website to find information and resources to assist with navigating online classes. Online student services are open. Learn more at the Resources for Students page.

Campus is closed. All in-person classes, labs and meetings are suspended. Faculty and Staff can see full details at the Instructional Transition page. An introduction to single-variable differential and integral calculus including: functions, limits and continuity; techniques and applications of differentiation and integration; the Fundamental Th eorem of Calculus; areas and volumes of solids of revolution.

Students are also strongly encouraged to take advantage of the many resources available to support them at LPC. Continuation of single-variable differential and integral calculus. Topics covered include: inverse and hyperbolic functions; techniques of integration; polar and parametric equations; infinite sequences, series, power series and Taylor series; applications of integration. Primarily for mathematics, physical science and engineering majors.

Introduction to diff erential equations including the conditions under which a unique solution exists, techniques for obtaining solutions, and applications.

Techniques include generation of series solutions, use of Laplace Transforms, and the use of eigenvalues to solve linear systems. An introduction to linear algebra including: techniques and theory needed to solve and classify systems of linear equations using Gaussian elimination and matrix algebra; properties of vectors in n-dimensions; generalized vector spaces, inner product spaces, basis, norms, orthogonality; eigenvalues, eigenspaces; and linear transformations.

Designed for majors in mathematics and computer science, this course provides an introduction to discrete mathematical structures used in Computer Science and their applications.

math 55b pdf

Course content includes: Propositional and predicate logic; rules of inference; quantifiers; elements of integer number theory; set theory; methods of proof; induction; combinatorics and discrete probability; functions and relations; recursive definitions and recurrence relations; elements of graph theory and trees. Applications include: analysis of algorithms, Boolean algebras and digital logic circuits. Students who have completed, or are enrolled in, CS 17 may not receive credit.

College algebra core concepts relating to Science, Technology, Engineering and Mathematics STEM and Business fields are explored, such as: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; and analytic geometry. Multiple representations, applications and modeling with functions are emphasized throughout. May not receive credit if Mathematics 20 or 45 have been completed.

Beginning Fallstudents are encouraged to enroll directly into a transfer-level course. Students should consider their academic goal, past achievements, and experiences.

Linear functions, systems of linear equations and inequalities, exponential and logarithmic functions and applications, matrices, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

All Categories. Grade Level. Resource Type. Log In Join Us. View Wish List View Cart. Holt Algebra 5. MathAlgebra. Grade Levels. WorksheetsTest PrepHomework. File Type. Product Description. This r squared creation is the complementary worksheet for our 5. This worksheet is practice for the students on how to put any equation into slope-intercept form and how to graph an equation using the slope and y-intercept when NOT in slope-intercept form. The zip file contains the worksheet in both.

Save money by purchasing the worksheet plus its corresponding PowerPoint together. Or save even more by buying the entire Chapter 5A bundle or the Fall Semester package. CA Standard: 6. Total Pages.

Babylonian Talmud: Tractate Sanhedrin

Report this Resource to TpT. Reported resources will be reviewed by our team. Add one to cart. Buy licenses to share.Please Note: These Products are only available for purchase by homeschools, consumers, and public institutions. Saxon's Math 2 kit continues teaching young minds in an incremental manner, slowly building upon previously learned concepts and increasing retention. Math 2 covers working with larger numbers, geometric shapes, Venn diagrams, graphs, basic calculations, simple fractions and multi-step problems.

This kit includes: Meeting Book page teacher's manual Student workbook with practice pages, masters and fact cards. The Manipulatives Kit is required and sold separately. The Meeting Book is a calendar used to keep track of your child's progress.

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Record "meetings" from Saxon Math Level 2. Help build your children's foundation for practical and academic math skills with saxon's incremental approach to learning.

Constant review and practice keeps concepts fresh and ready to be built upon by subsequent lessons. This two workbook kit includes worksheets and corresponding assessment forms. Color-coded fact cards will also give your child plenty of practice in addition, subtraction, multiplication and division.

Three-hole-punched, softcover. Meeting Books not included and sold-separately. The key to math success for your irrepressible hands-on learners! Designed to complement Saxon Math programs for grades K to 3, this home study kit includes a set of 55 dominoes, "color tiles," 2 geoboards with rubber bands, 2 plastic clocks, assorted tangrams and colorful plastic shapes, 2 standard rulers, a student balance, teddy bear counters, and more.

This kit contains the manipulatives you'll need for introducing and reinforcing the math concepts taught in the Saxon Mathematics K-3 program. Perfect for kinesthetic learners, the hands-on activities will help with comprehension and mastery of foundational math concepts.

Kit contains: 48 baby bear counters, color tiles, a complete set of double nine dominoes, 2 geoboards with rubber bands, 1 hundred number board, linking cubes, pattern blocks, 1 primary balance, 2 rulers, 2 student clocks, 1 set of four tangrams, 25 two-color counting discs. You can unsubscribe at any time.

math 55b pdf

Enter email address. Welcome to Christianbook. Sign in or create an account. Search by title, catalog stockauthor, isbn, etc.Login Register. Section 1. Exam Review Solutions. Introduction to Calculus. Limit and Derivatives. Chapter Logs and Exponential Functions. Test - FloridaMAO. Primitive and General Recursive Functions.

Math Mornings: Chaos on the Circle, by Taylor McAdam

Mathematics Laboratory Manual. Math 55b Lecture Notes Contents. Section 2. There are three most common inverse trigonometric functions. Solve each equation. State the number and type of roots.

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Derivative The derivative of a function of a real variable measures the sensitivity to change of a quantity a function value or dependent variable which is determined by another quantity the independent variable. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced. The derivative of a function of a single variable at a chosen input value is the slope of the tangent line to the graph of the function at that point.

This means that it describes the best linear approximation of the function near that input value. For this reason, the derivative is often described as the ""instantaneous rate of change"", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is after an appropriate translation the best linear approximation to the graph of the original function.

The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables.

For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. The process of finding a derivative is called differentiation.Nahman, son of R. Hisda stated in an exposition: In the case of a woman, there are two modes of intimacy, but in the case of a beast, only one. Papa objected: On the contrary, since sexual intercourse with a woman is a natural thing, guilt should be incurred only for a natural connection, but for nothing else, whilst, since a connection with a beast is an unnatural thing, one should be punished for every such act, however it be done.

Is it not written, Thou shalt not lie with mankind as with womankind? Ahdaboi b. Ammi propounded a problem to R.

Shesheth: What if one excited himself to the first stage [of masturbation]? Ashi said: What is your problem?

Differential and integral inequalities; theory and applications PART B

This is impossible in self-stimulation; but it is possible in the case of coition with a membrum mortuum. On the view that such, in incest, is not punishable, in masturbation too it is not punishable. But on the view that it is punishable, a twofold penalty is incurred here, since he is simultaneously the active and passive partner of the deed.

It was asked of R. Shesheth: What if a heathen committed bestiality [is the animal killed or not]? We are speaking of living creatures, for which the All-Merciful One shewed pity. Come and hear! Now surely, To Part b Original footnotes renumbered. A male, aged nine years and a day who commits etc. The first — a male aged nine years and a day — refers to the passive subject of pederasty, the punishment being incurred by the adult offender. This must be its meaning — because firstly, the active offender is never explicitly designated as a male, it being understood, just as the Bible states, Thou shalt not lie with mankind, where only the sex of the passive participant is mentioned; and secondly, if the age reference is to the active party, the guilt being incurred by the passive adult party, why single out pederasty: in all crimes of incest, the passive adult does not incur guilt unless the other party is at least nine years and a day?

Hence the Baraitha supports Rab's contention that nine years and a day is the minimum age of the passive partner for the adult to be liable. The reference is to bestiality. If a woman allows herself to be made the subject thereof, whether naturally or not, she is guilty. But if a man commits bestiality, he is liable only for a connection in a natural manner, but not otherwise.

Thus Rashi.Even this dream that was ultimately fulfilled contained an element that was not fulfilled. From the same source, Rabbi Levi said: One should always anticipate fulfillment of a good dream up to twenty-two years after the dream.

From where do we derive this? From seventeen to thirty how many years are they? Thirteen; and add seven years of plenty and two of famine; the total is twenty-two and only then was the dream fulfilled when his brothers came and bowed down to him. Rav Huna said: A good person is not shown a good dream and a wicked person is not shown a bad dream; rather, a good person is punished for his relatively few transgressions with bad dreams and a wicked person is rewarded for his relatively few merits with good dreams.

Neither shall any plague come near your tent, means that you will never find your wife with the uncertain status of a menstruating woman when you return from a journey.

This proves that it is impossible that a righteous person will experience bad dreams throughout his life. Rather, one might say that he does not see bad dreams; others see bad dreams about him. The Gemara asks: And when he does not see a dream, is that a virtue? Rather, one must say that David saw dreams and the baraita says as follows: David certainly saw dreams, but he did not understand what he saw. The Gemara is surprised by this: Interpreted?

If one is concerned about a dream, why would he actively promote its fulfillment? Rather, say as follows: He should better it before three. He should bring three people and say to them: I saw a good dream.

And they should say to him: It is good, and let it be good, may God make it good. May they decree upon you from heaven seven times that it will be good, and it will be good. Afterwards they recite three verses of transformation from bad to good, three verses of redemption, and three verses which mention peace.

They said: Let each and every one of us say something that the other has not heard.

math 55b pdf

One of them began and said: One who saw a dream and does not know what he saw should stand before the priests when they lift their hands during the Priestly Blessing and say the following: Master of the Universe, I am Yours and my dreams are Yours, I dreamed a dream and I do not know what it is.

Whether I have dreamed of myself, whether my friends have dreamed of me or whether I have dreamed of others, if the dreams are good, strengthen them and reinforce them like the dreams of Joseph.

And if the dreams require healing, heal them like the bitter waters of Mara by Moses our teacher, and like Miriam from her leprosy, and like Hezekiah from his illness, and like the bitter waters of Jericho by Elisha. And just as You transformed the curse of Balaam the wicked into a blessing, so transform all of my dreams for me for the best.

And he should complete his prayer together with the priests so the congregation responds amen both to the blessing of the priests and to his individual request. And if he is not able to recite this entire formula, he should say: Majestic One on high, Who dwells in power, You are peace and Your name is peace. May it be Your will that You bestow upon us peace. Do not read it as alei ayin ; but rather, read it as olei ayinwho rise above the eye and the evil eye has no dominion over him.

And if he is concerned about his own evil eye, lest it damage others, he should look at the side of his left nostril. Another began and said: One who is sick should not reveal it on the first day of his illness so that his luck should not suffer; from there on he may reveal it.

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Like that which Rava does when he falls ill; on the first day he does not reveal it, from there on he says to his servant: Go out and announce: Rava is sick. Those who love me will pray that God have mercy on me and those who hate me will rejoice over my distress.

The joy of my enemy over my distress will also assist my healing. When he would see a good dream, he would say: And do dreams speak falsely? One time, I dreamed a dream and went to each of them to interpret it. What one interpreted for me the other did not interpret for me, and, nevertheless, all of the interpretations were realized in me, to fulfill that which is stated: All dreams follow the mouth of the interpreter.

The Gemara asks: Is that to say that all dreams follow the mouth is a verse cited as corroboration? The Gemara responds: Yes, and in accordance with the opinion of Rabbi Elazar, as Rabbi Elazar said: From where is it derived that all dreams follow the mouth of the interpreter?Neuroscience, the study of the nervous system, is a field that investigates the biological mechanisms that underlie behavior and how brains process information.

To develop a comprehensive understanding, we study the nervous system at every level: from the macroscopic behavior and cognition to the microscopic cells and molecules. Consequently, the questions that neuroscientists ask are wide-ranging. For example, how do electrical, chemical, and molecular signals allow neurons to process and transmit information from the environment?

What guides the development of the immense number of precise connections in the nervous system? How can the complex signals of many thousands of active neurons be recorded, interpreted, and modeled? To answer these kinds of questions, neuroscientists study a variety of model systems including cultured cells, fruit flies, zebrafish, mice, monkeys, and humans.

Simpler systems allow experimental manipulations e. Studies in humans often focus on characterizing patterns of brain activity during development or disease using non-invasive recording techniques e.

Neuroscientists may also use approaches from computer science and mathematics to analyze signals that arise from the brain or to understand the computational properties of neural networks. Thus, the study of neuroscience provides both a broad scientific training and a deep understanding of the biology of the nervous system. Given the diversity of interests in this field, the only prerequisite for students entering this concentration is an intense curiosity about the brain.

The Neuroscience curriculum includes a series of fundamental courses in the life and applied sciences. A central course on the neurobiology of behavior, Neuro 80 formerly MCB 80lays out the body of knowledge in neuroscience. In advanced elective courses, students explore specific areas of neuroscience more deeply based on their interests.

We now list over 40 advanced courses on a range of topics: cells and circuits, physiology, learning and memory, cognitive science, development, genetics, computational modeling, and disease and therapeutics. In addition to the course offerings, neuroscience is one of the most vibrant fields of research at Harvard, and students have many opportunities for hands-on laboratory experience and independent research projects to complement and deepen their studies.

We offer three tracks within the Neuroscience concentration.

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For this track, Honors is optional. This is an Honors track and requires an undergraduate thesis. Students interested in a joint concentration should consult the advisers in both concentrations at an early date.